Littérature scientifique sur le sujet « Principle of minimum entropy production »

AbstractAn essential problem in snow science is to predict the changing form of ice grains within a snow layer. Present theories are based on the idea that form changes are driven by mass diffusion induced by temperature gradients within the snow cover. This leads to the well-established theory of isothermal- and temperature-gradient metamorphism. Although diffusion theory treats mass transfer, it does not treat the influence of this mass transfer on the form — the curvature radius of the grains and bonds — directly. Empirical relations, based on observations, are additionally required to predict flat or rounded surfaces. In the following, we postulate that metamorphism, the change of ice surface curvature and size, is a process of thermodynamic optimization in which entropy production is minimized. That is, there exists an optimal surface curvature of the ice grains for a given thermodynamic state at which entropy production is stationary. This state is defined by differences in ice and air temperature and vapor pressure across the interfacial boundary layer. The optimal form corresponds to the state of least wasted work, the state of minimum entropy production. We show that temperature gradients produce a thermal non-equilibrium between the ice and air such that, depending on the temperature, flat surfaces are required to mimimize entropy production. When the temperatures of the ice and air are equal, larger curvature radii are found at low temperatures than at high temperatures. Thus, what is known as isothermal metamorphism corresponds to minimum entropy production at equilibrium temperatures, and so-called temperature-gradient metamorphism corresponds to minimum entropy production at none-quilibrium temperatures. The theory is in good agreement with general observations of crystal form development in dry seasonal alpine snow.

Forest ecosystems are vivid representatives of open non-equilibrium systems. The existence of extreme principles in “ecological thermodynamics” is a subject of discussion in the works of many physicists, ecologists and researchers dealing with non-equilibrium thermodynamics. At the same time, the problem of the connection between the principles of maximum and minimum entropy production has been studied in detail enough in the works of L. M. Martyushev et al. However, for forest ecosystems, the works that point out the connection of these fundamental principles are clearly insufficient. Usually, these principles are opposed to each other. In the proposed work, within the framework of a unified approach, the dependencies of the entropy production density and the entropy density have modeled using the example of a pine (Pínus sylvestris) stand of the 1-grade forest site capacity. It has shown that entropy production and entropy production density take both maximum and minimum values in the process of ecosystem evolution.

The article gives a thermodynamic substantiation of the direction of nonequilibrium processes in tribocouples of machine parts, in tribosystems, based on the principles of maximum and minimum entropy. It is clarified how nonequilibrium processes can be substantiated on the basis of the minimum and maximum function of entropy production: linear and nonlinear nonequilibrium processes and their different thermodynamics. The entropy production function is considered as a function of thermodynamic force flows and thermodynamic flows. The theory of nonequilibrium processes is based on the Liouville equation for classical tribosystems, taking into account external influences or perturbations. It is shown that in thermodynamic processes in tribosystems the principle of entropy maximization is realized as the second principle of synergetics.

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics.

In this paper separation-induced shock reflection is studied theoretically and experimentally. An analytical model is proposed to establish the connections among upstream conditions, downstream conditions and shock configurations. Furthermore, the minimum entropy production principle is employed to determine the incident shock angles as well as the criterion for the transition from regular reflection to Mach reflection, which agrees well with experimental results. Additionally, a solution path for a reflected shock that fulfills the minimum entropy production principle is found in the overall regular reflection domain, based on which the steadiest shock configuration may be determined according to upstream and downstream conditions.

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.

La thermodynamique des processus hors équilibre est reconnue de longue date comme un lieu de prédilection de la modélisation des conversions de l’énergie. Initialement développée par Sadi Carnot pour optimiser l’utilisation des machines à vapeur durant l’essor de l’ère industrielle, la modélisation de la conversion thermodynamique a connu de nombreux développements, dont en particulier ceux de Lars Onsager puis Herbert Callen, et enfin Prigogine. Au cœur de ces développements se trouve la question de la puissance extractible, question qui ne peut être abordée par la thermostatique mais par la thermodynamique à temps fini. Cette dernière, formulée depuis le milieu du siècle dernier par Novikov et Chambadal, a été remise en lumière par Curzon et Ahlborn dans les années 1970 sous la forme des machines endoréversibles. Dans ce cadre où l’évolution d’un système est gouvernée par les gradients des grandeurs intensives, il devient possible de modéliser complètement le comportement des machines, les puissances produites et les entropies créées, dépassant ainsi le simple cadre endoréversible. Dans le cas de systèmes décrits par une seule grandeur intensive, le comportement retrouvé est celui des lois empiriques simples telles que les lois d’Ohm, de Fourier ou de Darcy. Lorsque plusieurs grandeurs intensives couplées sont en jeu, le comportement devient complexe à modéliser, surtout si le système présente des inhomogénéités des propriétés physiques du fluide de travail thermodynamique. Le travail mené au cours de cette thèse traite de ces questions. Il est basé sur la conception d’un simulateur de réseaux thermodynamiques, appliqués spécifiquement à la thermoélectricité, qui est un système modèle particulièrement fructueux. Le système est décrit par les relations force-flux et une approche en volume fini, ce qui permet de reconstruire un réseau thermodynamique fidèle au système étudié. Cette approche prend rigoureusement en compte l’hypothèse de continuité des grandeurs intensives entre chaque élément de volume, dont sa validité est tout d’abord démontrée en considérant la fluctuation de la production d’entropie et son caractère résiduel en situation stationnaire. Ce résultat est discuté dans le cadre du débat sur les questions de principe de minimisation de production d’entropie. Cette approche a été validée par plusieurs simulations de réseaux thermoélectriques dans différents régimes, qu’ils soient stationnaires, transitoires et harmoniques. La réponse obtenue contient les termes électriques et thermiques à la fois linéaires et non linéaires, ces derniers résultant des couplages énergie-matière. Ce simulateur a permis d’intégrer des matériaux dont la conductivité thermique peut être modulé tel que dans des matériaux férroélectriques. Les simulations transitoires incluant des matériaux à conductivité thermique modulable permettent ainsi de déterminer le temps de redistribution de la chaleur dans le réseau à la suite de cette modulation. Ces travaux ouvrent la voie à des simulations thermoélectriques complexes et peu accessibles par d’autres voies, telle que l’étude et le dimensionnement de modules thermoélectriques hétérogènes. L’intégration de la description locale sur le volume permet de faire émerger un comportement global issu de la prise en compte d’effets d’inclusions sur le couplage, suggérant de nouvelles perspectives de développement, tel que dans le cadre d’effets thermomagnétiques issus d’inhomogénéités
In this context, where the evolution of a system is governed by the gradients of intensive quantities, it becomes possible to completely model the behavior of machines, the produced power, and the created entropy, thus surpassing the simple endoreversible framework. In the case of systems described by a single intensive quantity, the behavior found is that of simple empirical laws such as Ohm’s law, Fourier’s law, or Darcy’s law. When several coupled intensive quantities are involved, the behavior becomes complex to model, especially if the system exhibits inhomogeneities in the physical properties of the working fluid. The work carried out in this thesis addresses these issues. It is based on the design of a thermodynamic network simulator, specifically applied to thermoelectricity, which is a particularly fruitful model system. The system is described by force-flux relations and a finite volume approach, which allows for the reconstruction of a thermodynamic network faithful to the studied system. This approach rigorously takes into account the hypothesis of continuity of intensive quantities between each volume element, whose validity is first demonstrated by considering the fluctuation of entropy production and its residual character in a stationary situation. This result also helped clarify the debate on the principles of entropy production minimization, a debate that still stirs part of the scientific community. This approach was validated by several simulations of thermoelectric networks in various regimes, stationary, transient, and harmonic. The obtained response includes both linear and nonlinear electrical and thermal terms, the latter resulting from energy-matter couplings. Beyond thermoelectricity, this simulator made it possible to integrate ferroelectric and antiferroelectric materials, whose thermal conductivity varies according to polarization. Transient simulations including materials with modifiable thermal conductivity thus allow determining the heat redistribution time in the network following this modulation. This work paves the way for complex thermoelectric simulations that are not accessible by other means, such as the study and design of heterogeneous thermoelectric modules. The integration of local description over volume allows for the emergence of global behavior resulting from the consideration of exotic inclusion effects on coupling, suggesting new development perspectives, notably in the context of thermomagnetic effects arising from local current loops

In questa tesi tratteremo il problema di costruire una teoria termodinamica per trasformazioni su un sistema passante per stati di non-equilibrio. Cercando di generalizzare a sistemi che non sono all’equilibrio, rilasseremo la richiesta che siano in equilibrio globalmente. Lo stato termodinamico sarà univocamente determinato da un insieme di parametri termodinamici definiti localmente, della stessa natura e significato fisico dei parametri usati nella termodinamica classica. Le molteplici assunzioni necessarie al fine di avere una teoria mesoscopica comunque predittiva verranno giustificate a posteriori, quando possibile, in base alle predizioni che da tale modello nasceranno. In particolare ci concentreremo sugli effetti termoelettrici di Thompson, Seebeck e Peltier, esempi storici di grande rilevanza nel campo della termodinamica del non-equilibrio.

Decomposition methods based on the hierarchical partitioning of the state space of queueing network models offer powerful evaluation tools for the performance analysis of computer systems and communication networks. These methods being conventionally implemented capture the exact solution of separable queueing network models but their credibility differs when applied to general queueing networks. This thesis provides a universal information theoretic framework for the implementation of hierarchical decomposition schemes, based on the principle of minimum relative entropy given fully decomposable subset and aggregate utilization, mean queue length and flow-balance constraints. This principle is used, in conjuction with asymptotic connections to infinite capacity queues, to derive new closed form approximations for the conditional and marginal state probabilities of general queueing network models. The minimum relative entropy solutions are implemented iteratively at each decomposition level involving the generalized exponential (GE) distributional model in approximating the general service and asymptotic flow processes in the network. It is shown that the minimum relative entropy joint state probability, subject to mean queue length and flow-balance constraints, is identical to the exact product-form solution obtained as if the network was separable. An investigation into the effect of different couplings of the resource units on the relative accuracy of the approximation is carried out, based on an extensive experimentation. The credibility of the method is demonstrated with some illustrative examples involving first-come-first-served general queueing networks with single and multiple servers and favourable comparisons against exact solutions and other approximations are made.

Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...

The principle of minimum entropy production is applied to the analysis of the formation of a solid structure in the course of the eutectic solidification. It is assumed that the liquid and solid phases are divided by the plane boundary and the solidification rate is constant. At these conditions solidification results in the development of the lamellar structure in the solid and the process is defined by the lamellar spacing and the rate of the motion of the liquid-solid interface. The variational equation describing system evolution is modified to describe the process in question. A solution of this equation determines the relationship between the solidification rate and the lamellar spacing. The obtained results complies with experimental data.

The principle of minimum entropy production has played an important role in the development of non-equilibrium thermodynamics. Inspired by this principle, Bejan derived the expression of the local entropy production rate for heat convection and established the entropy production minimization approach for the heat exchanger optimization design. Although one can obtain the entropy production distribution in the heat exchanger numerically, it can not directly been employed to examine the heat exchanger performance. Tondeur and Kvaalen found that the entropy production uniformity is closely related to the heat exchanger performance. In the present work, based on Tondear and Kvaalen’s work, an entropy production uniformity factor is defined, which quantifies the uniformity of the local entropy generation distribution in heat exchanger. Numerical results of the heat transfer in a rectangular channel show that the larger entropy production uniformity factor implies less irreversible loses. Therefore, this factor can serve as a thermodynamic figure of merit for assessing the heat exchanger performance.

Abstract In order to optimize the flow and heat transfer of solar collectors and heat exchangers that use molten salts NaCl-KCl-MgCl2 or KCl-MgCl2, entropy generation minimization principle is used as the criterion. Gnielinski correlation and Dittus-Bölter correlation for Nusselt number versus Reynolds number as well as Moody friction factor given by Petukhov were used for the calculation of heat transfer coefficient and pressure loss due to friction. The objective function, the entropy production of the heat transfer system, was expressed as the function of Reynolds number, Prandtl number, heating flux, pipe diameter, etc. The minimum entropy production could be found from the first order deviation of the entropy production versus Reynolds number. As a result of the analysis, the optimum Reynolds number was determined and thereby determined the optimum Nusselt number, convective heat transfer coefficient, friction factor, and tube diameter, which helps the selection of optimum flow velocities and diameter of fluid pipes. The analysis was conducted in the fluid temperature range of 550 °C to 700 °C which covers the operation temperature for supercritical CO2 cycles. Results from using different heat transfer correlations (Gnielinski correlation and Dittus-Bölter correlation) have been compared and some obvious deviations were identified. It indicates that the selection of heat transfer correlations can cause some deviation of the optimal parameters of Reynolds number and pipe diameter. From the researcher’s experience and experimental studies to molten chloride salts heat transfer, Gnielinski correlation for heat transfer is favorably recommended.

The problem of determining the optimal configuration of a cooled gas-turbine blade is approached by an entropy minimization technique proposed in previous works by the same authors. The present paper describes the application of the same line of thought to a more complex (and realistic) pseudo-optimization procedure, in which the objective function is again the global entropy generation rate, but two integral constraints are added to the original formulation: the maximum blade temperature (weak constraint) and the overall enthalpy drop of the working fluid in the blade passage (strong constraint). The discontinuous optimization procedure is presented here in an application which resembles a trial-and-error technique, but can be rigorously and formally described and implemented [12]. As a “zero configuration”, a realistic 2-D geometry is considered, and the thermo-fluiddynamic field around it is computed via a standard finite-element code. Then, the entropy generation rates in the blade/fluid system are calculated, and the value of the overall enthalpy drop of the gas as well as the value and location of the maximum blade temperature are recorded. Keeping all other parameters fixed (in particular, maintaining the same cooling air flowrate), the geometry of the blade is slightly “perturbed”, by introducing arbitrary modifications in the blade profile, the number and location of cooling holes, etc. Again, the velocity and temperature fields are computed, and inlet conditions are tuned so that the overall enthalpy drop remains approximately constant and the blade maximum temperature does not exceed a certain assigned value. An “optimal” configuration is found, which is affected by the minimal entropy generation rate, while abiding to the imposed constraints. The procedure is demonstrated on a realistic blade profile, and is shown to produce a better performing cascade, at least in this 2-D simulation. The extension to 3-D problems is — in principle — straightforward (but see Section 3 for further comments).

In order to improve the performance of compact heat exchangers engineers and researchers explore different passive techniques of flow manipulation. Among them one can find the delta wing shaped longitudinal vortex generator. In order to assess the optimal shape of finned tube heat exchangers, the engineer has at disposal many coefficients, such as the Colburn factor j and friction factor f. In the present paper the second law of thermodynamics is introduced to explore the flow and thermal field generated by punched longitudinal vortex generators shaped as winglets around an oval tube. The winglets are in common flow up configuration near the leading edge of the fin. Not only the heat transfer and fluid flow characteristics are studied, but also the local irreversibility methodology is applied to predict the two components of entropy generation rate: the one caused by direct dissipation and the other due to heat transfer. The flow velocity and temperature are numerically determined by solving the Navier-Stokes and energy equations with a finite volume method. The local entropy production is then calculated with the use of available information from the solved flow and thermal fields. This paper is based on Chen works. He has studied the flow characteristics for such a geometrical configuration. But here the fin efficiency is supposed to be equal to the unity. The influence of the angle of attack of winglets on the entropy production is studied. Three elemental configurations are displayed. Each one corresponds respectively to an angle of attack β equal to 20°, 30° and 45°. The minimal entropy principle is adopted to evaluate a global heat exchanger build up as a pile up of elemental component.

The technology and procedures for the inspection of pipelines from offshore production and process facilities to shore or other offshore installations has developed rapidly in recent years. This rapid development can be attributed to several factors including pipeline operators protecting their investment in their lines, heightened environmental protection concerns, and increasing regulatory requirements. A limited number of the offshore pipeline systems in the U.S. currently include the ability to inspect the trunkline using either an ultrasonic or magnetic particle inspection pig. This pig is moved through the pipeline with the product flow from the trunkline's point of origin offshore to an onshore or nearshore facility. As the pig moves through the line, it takes and stores measurement readings which can be downloaded and interpreted after the pig is removed from the line. While inspection pig technology can provide the pipeline operator with valuable information, several factors can prohibit development of a successful trunkline inspection pigging program. Because inspection pigs have onboard data measurement and storage facilities, they are significantly longer and heavier than foam or scraper pigs, and must be articulated to negotiate pipe bends. The minimum negotiable bend radius varies among inspection pig vendors, but is typically between 3 - 5 pipe diameters. The drive cups on an articulated pig are located in the front to prevent buckling. The cups must maintain a close fit with the inside pipe diameter to propel the pig through the pipeline and can stall or jam in a multi-diameter pipeline. The scope of the project includes the development of several basic concepts which, in principle, meet the project objectives. These concepts have been evaluated from several technical viewpoints and two primary concepts selected for further development. A preliminary design effort, carried out on both primary concepts, includes: Structure stress calculations; Detailed layouts of major assemblies and components Step by step installation, operation, and maintenance procedures; Detailed capital and operating cost development. A basic scenario of a 12"� ANSI 900# rated system in 400 ft. water depth is used for both concepts. A sensitivity analysis for the effects of greater and lesser water depths (800 ft. and 100 ft.) and a change in pipe size to 8"� nominal is also included.

Banco de la República is celebrating its 100th anniversary in 2023. This is a very significant anniversary and one that provides an opportunity to highlight the contribution the Bank has made to the country’s development. Its track record as guarantor of monetary stability has established it as the one independent state institution that generates the greatest confidence among Colombians due to its transparency, management capabilities, and effective compliance with the central banking and cultural responsibilities entrusted to it by the Constitution and the Law. On a date as important as this, the Board of Directors of Banco de la República (BDBR) pays tribute to the generations of governors and officers whose commitment and dedication have contributed to the growth of this institution.1 Banco de la República’s mandate was confirmed in the National Constitutional Assembly of 1991 where the citizens had the opportunity to elect the seventy people who would have the task of drafting a new constitution. The leaders of the three political movements with the most votes were elected as chairs to the Assembly, and this tripartite presidency reflected the plurality and the need for consensus among the different political groups to move the reform forward. Among the issues considered, the National Constitutional Assembly gave special importance to monetary stability. That is why they decided to include central banking and to provide Banco de la República with the necessary autonomy to use the instruments for which they are responsible without interference from other authorities. The constituent members understood that ensuring price stability is a state duty and that the entity responsible for this task must be enshrined in the Constitution and have the technical capability and institutional autonomy necessary to adopt the decisions they deem appropriate to achieve this fundamental objective in coordination with the general economic policy. In particular, Article 373 established that “the State, through Banco de la República, shall ensure the maintenance of the purchasing power of the currency,” a provision that coincided with the central banking system adopted by countries that have been successful in controlling inflation. In 1999, in Ruling 481, the Constitutional Court stated that “the duty to maintain the purchasing power of the currency applies to not only the monetary, credit, and exchange authority, i.e., the Board of Banco de la República, but also those who have responsibilities in the formulation and implementation of the general economic policy of the country” and that “the basic constitutional purpose of Banco de la República is the protection of a sound currency. However, this authority must take the other economic objectives of state intervention such as full employment into consideration in their decisions since these functions must be coordinated with the general economic policy.” The reforms to Banco de la República agreed upon in the Constitutional Assembly of 1991 and in Act 31/1992 can be summarized in the following aspects: i) the Bank was assigned a specific mandate: to maintain the purchasing power of the currency in coordination with the general economic policy; ii) the BDBR was designatedas the monetary, foreign exchange, and credit authority; iii) the Bank and its Board of Directors were granted a significant degree of independence from the government; iv) the Bank was prohibited from granting credit to the private sector except in the case of the financial sector; v) established that in order to grant credit to the government, the unanimous vote of its Board of Directors was required except in the case of open market transactions; vi) determined that the legislature may, in no case, order credit quotas in favor of the State or individuals; vii) Congress was appointed, on behalf of society, as the main addressee of the Bank’s reporting exercise; and viii) the responsibility for inspection, surveillance, and control over Banco de la República was delegated to the President of the Republic. The members of the National Constitutional Assembly clearly understood that the benefits of low and stable inflation extend to the whole of society and contribute mto the smooth functioning of the economic system. Among the most important of these is that low inflation promotes the efficient use of productive resources by allowing relative prices to better guide the allocation of resources since this promotes economic growth and increases the welfare of the population. Likewise, low inflation reduces uncertainty about the expected return on investment and future asset prices. This increases the confidence of economic agents, facilitates long-term financing, and stimulates investment. Since the low-income population is unable to protect itself from inflation by diversifying its assets, and a high proportion of its income is concentrated in the purchase of food and other basic goods that are generally the most affected by inflationary shocks, low inflation avoids arbitrary redistribution of income and wealth.2 Moreover, low inflation facilitates wage negotiations, creates a good labor climate, and reduces the volatility of employment levels. Finally, low inflation helps to make the tax system more transparent and equitable by avoiding the distortions that inflation introduces into the value of assets and income that make up the tax base. From the monetary authority’s point of view, one of the most relevant benefits of low inflation is the credibility that economic agents acquire in inflation targeting, which turns it into an effective nominal anchor on price levels. Upon receiving its mandate, and using its autonomy, Banco de la República began to announce specific annual inflation targets as of 1992. Although the proposed inflation targets were not met precisely during this first stage, a downward trend in inflation was achieved that took it from 32.4% in 1990 to 16.7% in 1998. At that time, the exchange rate was kept within a band. This limited the effectiveness of monetary policy, which simultaneously sought to meet an inflation target and an exchange rate target. The Asian crisis spread to emerging economies and significantly affected the Colombian economy. The exchange rate came under strong pressure to depreciate as access to foreign financing was cut off under conditions of a high foreign imbalance. This, together with the lack of exchange rate flexibility, prevented a countercyclical monetary policy and led to a 4.2% contraction in GDP that year. In this context of economic slowdown, annual inflation fell to 9.2% at the end of 1999, thus falling below the 15% target set for that year. This episode fully revealed how costly it could be, in terms of economic activity, to have inflation and exchange rate targets simultaneously. Towards the end of 1999, Banco de la República announced the adoption of a new monetary policy regime called the Inflation Targeting Plan. This regime, known internationally as ‘Inflation Targeting,’ has been gaining increasing acceptance in developed countries, having been adopted in 1991 by New Zealand, Canada, and England, among others, and has achieved significant advances in the management of inflation without incurring costs in terms of economic activity. In Latin America, Brazil and Chile also adopted it in 1999. In the case of Colombia, the last remaining requirement to be fulfilled in order to adopt said policy was exchange rate flexibility. This was realized around September 1999, when the BDBR decided to abandon the exchange-rate bands to allow the exchange rate to be freely determined in the market.Consistent with the constitutional mandate, the fundamental objective of this new policy approach was “the achievement of an inflation target that contributes to maintaining output growth around its potential.”3 This potential capacity was understood as the GDP growth that the economy can obtain if it fully utilizes its productive resources. To meet this objective, monetary policy must of necessity play a countercyclical role in the economy. This is because when economic activity is below its potential and there are idle resources, the monetary authority can reduce the interest rate in the absence of inflationary pressure to stimulate the economy and, when output exceeds its potential capacity, raise it. This policy principle, which is immersed in the models for guiding the monetary policy stance, makes the following two objectives fully compatible in the medium term: meeting the inflation target and achieving a level of economic activity that is consistent with its productive capacity. To achieve this purpose, the inflation targeting system uses the money market interest rate (at which the central bank supplies primary liquidity to commercial banks) as the primary policy instrument. This replaced the quantity of money as an intermediate monetary policy target that Banco de la República, like several other central banks, had used for a long time. In the case of Colombia, the objective of the new monetary policy approach implied, in practical terms, that the recovery of the economy after the 1999 contraction should be achieved while complying with the decreasing inflation targets established by the BDBR. The accomplishment of this purpose was remarkable. In the first half of the first decade of the 2000s, economic activity recovered significantly and reached a growth rate of 6.8% in 2006. Meanwhile, inflation gradually declined in line with inflation targets. That was how the inflation rate went from 9.2% in 1999 to 4.5% in 2006, thus meeting the inflation target established for that year while GDP reached its potential level. After this balance was achieved in 2006, inflation rebounded to 5.7% in 2007, above the 4.0% target for that year due to the fact that the 7.5% GDP growth exceeded the potential capacity of the economy.4 After proving the effectiveness of the inflation targeting system in its first years of operation, this policy regime continued to consolidate as the BDBR and the technical staff gained experience in its management and state-of-the-art economic models were incorporated to diagnose the present and future state of the economy and to assess the persistence of inflation deviations and expectations with respect to the inflation target. Beginning in 2010, the BDBR established the long-term 3.0% annual inflation target, which remains in effect today. Lower inflation has contributed to making the macroeconomic environment more stable, and this has favored sustained economic growth, financial stability, capital market development, and the functioning of payment systems. As a result, reductions in the inflationary risk premia and lower TES and credit interest rates were achieved. At the same time, the duration of public domestic debt increased significantly going from 2.27 years in December 2002 to 5.86 years in December 2022, and financial deepening, measured as the level of the portfolio as a percentage of GDP, went from around 20% in the mid-1990s to values above 45% in recent years in a healthy context for credit institutions.Having been granted autonomy by the Constitution to fulfill the mandate of preserving the purchasing power of the currency, the tangible achievements made by Banco de la República in managing inflation together with the significant benefits derived from the process of bringing inflation to its long-term target, make the BDBR’s current challenge to return inflation to the 3.0% target even more demanding and pressing. As is well known, starting in 2021, and especially in 2022, inflation in Colombia once again became a serious economic problem with high welfare costs. The inflationary phenomenon has not been exclusive to Colombia and many other developed and emerging countries have seen their inflation rates move away from the targets proposed by their central banks.5 The reasons for this phenomenon have been analyzed in recent Reports to Congress, and this new edition delves deeper into the subject with updated information. The solid institutional and technical base that supports the inflation targeting approach under which the monetary policy strategy operates gives the BDBR the necessary elements to face this difficult challenge with confidence. In this regard, the BDBR reiterated its commitment to the 3.0% inflation target in its November 25 communiqué and expects it to be reached by the end of 2024.6 Monetary policy will continue to focus on meeting this objective while ensuring the sustainability of economic activity, as mandated by the Constitution. Analyst surveys done in March showed a significant increase (from 32.3% in January to 48.5% in March) in the percentage of responses placing inflation expectations two years or more ahead in a range between 3.0% and 4.0%. This is a clear indication of the recovery of credibility in the medium-term inflation target and is consistent with the BDBR’s announcement made in November 2022. The moderation of the upward trend in inflation seen in January, and especially in February, will help to reinforce this revision of inflation expectations and will help to meet the proposed targets. After reaching 5.6% at the end of 2021, inflation maintained an upward trend throughout 2022 due to inflationary pressures from both external sources, associated with the aftermath of the pandemic and the consequences of the war in Ukraine, and domestic sources, resulting from: strengthening of local demand; price indexation processes stimulated by the increase in inflation expectations; the impact on food production caused by the mid-2021 strike; and the pass-through of depreciation to prices. The 10% increase in the minimum wage in 2021 and the 16% increase in 2022, both of which exceeded the actual inflation and the increase in productivity, accentuated the indexation processes by establishing a high nominal adjustment benchmark. Thus, total inflation went to 13.1% by the end of 2022. The annual change in food prices, which went from 17.2% to 27.8% between those two years, was the most influential factor in the surge in the Consumer Price Index (CPI). Another segment that contributed significantly to price increases was regulated products, which saw the annual change go from 7.1% in December 2021 to 11.8% by the end of 2022. The measure of core inflation excluding food and regulated items, in turn, went from 2.5% to 9.5% between the end of 2021 and the end of 2022. The substantial increase in core inflation shows that inflationary pressure has spread to most of the items in the household basket, which is characteristic of inflationary processes with generalized price indexation as is the case in Colombia. Monetary policy began to react early to this inflationary pressure. Thus, starting with its September 2021 session, the BDBR began a progressive change in the monetary policy stance moving away from the historical low of a 1.75% policy rate that had intended to stimulate the recovery of the economy. This adjustment process continued without interruption throughout 2022 and into the beginning of 2023 when the monetary policy rate reached 12.75% last January, thus accumulating an increase of 11 percentage points (pp). The public and the markets have been surprised that inflation continued to rise despite significant interest rate increases. However, as the BDBR has explained in its various communiqués, monetary policy works with a lag. Just as in 2022 economic activity recovered to a level above the pre-pandemic level, driven, along with other factors, by the monetary stimulus granted during the pandemic period and subsequent months, so too the effects of the current restrictive monetary policy will gradually take effect. This will allow us to expect the inflation rate to converge to 3.0% by the end of 2024 as is the BDBR’s purpose.Inflation results for January and February of this year showed declining marginal increases (13 bp and 3 bp respectively) compared to the change seen in December (59 bp). This suggests that a turning point in the inflation trend is approaching. In other Latin American countries such as Chile, Brazil, Perú, and Mexico, inflation has peaked and has begun to decline slowly, albeit with some ups and downs. It is to be expected that a similar process will take place in Colombia in the coming months. The expected decline in inflation in 2023 will be due, along with other factors, to lower cost pressure from abroad as a result of the gradual normalization of supply chains, the overcoming of supply shocks caused by the weather, and road blockades in previous years. This will be reflected in lower adjustments in food prices, as has already been seen in the first two months of the year and, of course, the lagged effect of monetary policy. The process of inflation convergence to the target will be gradual and will extend beyond 2023. This process will be facilitated if devaluation pressure is reversed. To this end, it is essential to continue consolidating fiscal sustainability and avoid messages on different public policy fronts that generate uncertainty and distrust. 1 This Report to Congress includes Box 1, which summarizes the trajectory of Banco de la República over the past 100 years. In addition, under the Bank’s auspices, several books that delve into various aspects of the history of this institution have been published in recent years. See, for example: Historia del Banco de la República 1923-2015; Tres banqueros centrales; Junta Directiva del Banco de la República: grandes episodios en 30 años de historia; Banco de la República: 90 años de la banca central en Colombia. 2 This is why lower inflation has been reflected in a reduction of income inequality as measured by the Gini coefficient that went from 58.7 in 1998 to 51.3 in the year prior to the pandemic. 3 See Gómez Javier, Uribe José Darío, Vargas Hernando (2002). “The Implementation of Inflation Targeting in Colombia”. Borradores de Economía, No. 202, March, available at: https://repositorio.banrep.gov.co/handle/20.500.12134/5220 4 See López-Enciso Enrique A.; Vargas-Herrera Hernando and Rodríguez-Niño Norberto (2016). “The inflation targeting strategy in Colombia. An historical view.” Borradores de Economía, No. 952. https://repositorio.banrep.gov.co/handle/20.500.12134/6263 5 According to the IMF, the percentage change in consumer prices between 2021 and 2022 went from 3.1% to 7.3% for advanced economies, and from 5.9% to 9.9% for emerging market and developing economies. 6 https://www.banrep.gov.co/es/noticias/junta-directiva-banco-republica-reitera-meta-inflacion-3