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Books on the topic 'Boltzmann statistics'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Cercignani, Carlo. Ludwig Boltzmann e la meccanica statistica. La goliardica pavese, 1997.

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2

International Symposium "Boltzmann's Legacy" (2006 Vienna, Austria). Boltzmann's legacy. Edited by Gallavotti Giovanni, Reiter Wolfgang L, and Jakob Yngvason. European Mathematical Society, 2008.

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International Symposium "Boltzmann's Legacy" (2006 Vienna, Austria). Boltzmann's legacy. Edited by Gallavotti Giovanni, Reiter Wolfgang L, and Jakob Yngvason. European Mathematical Society, 2008.

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4

Giovanni, Gallavotti, Reiter Wolfgang L, and Jakob Yngvason, eds. Boltzmann's legacy. European Mathematical Society, 2008.

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5

1844-1906, Boltzmann Ludwig, ed. Boltzmann's legacy 150 years after his birth. Accademia nazionale dei Lincei, 1997.

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6

V, Karlin Ilya, ed. Invariant manifolds for physical and chemical kinetics. Springer, 2005.

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7

Quantum Statistics and the Boltzmann Equation. Creative Media Partners, LLC, 2023.

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8

Chance, Kelly, and Randall V. Martin. Blackbody Radiation, Boltzmann Statistics, Temperature, and Thermodynamic Equilibrium. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199662104.003.0003.

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Blackbody radiation, temperature, and thermodynamic equilibrium give a tightly coupled description of systems (atmospheres, volumes, surfaces) that obey Boltzmann statistics. They provide descriptions of systems when Boltzmann statistics apply, either approximately or nearly exactly. These apply most of the time in the Earth’s stratosphere and troposphere, and in other planetary atmospheres as long as the density is sufficient that collisions among atmospheric molecules, rather than photochemical and photophysical properties, determine the energy populations of the ensemble of molecules. Therm

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9

Porter, Theodore M. The Rise of Statistical Thinking, 1820-1900. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691208428.001.0001.

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This book explores the history of statistics from the field's origins in the nineteenth century through to the factors that produced the burst of modern statistical innovation in the early twentieth century. The book shows that statistics was not developed by mathematicians and then applied to the sciences and social sciences. Rather, the field came into being through the efforts of social scientists, who saw a need for statistical tools in their examination of society. Pioneering statistical physicists and biologists James Clerk Maxwell, Ludwig Boltzmann, and Francis Galton introduced statist

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10

Darrigol, Olivier. Constructing Thermal Equilibrium (1866–1871). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0003.

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This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal equilibrium, including the existence of the entropy function and the Maxwell–Boltzmann law, by various means including the principle of least action, Maxwell’s collision formula, the ergodic hypothesis, and a procedure of adiabatic variation. This is an immensely fertile period in which Boltzmann introduced several of the basic concepts, problems, and difficulties of modern statistical mechanics.

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11

Succi, Sauro. The Fluctuating Lattice Boltzmann. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0030.

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Fluid flow at nanoscopic scales is characterized by the dominance of thermal fluctuations (Brownian motion) versus directed motion. Thus, at variance with Lattice Boltzmann models for macroscopic flows, where statistical fluctuations had to be eliminated as a major cause of inefficiency, at the nanoscale they have to be summoned back. This Chapter illustrates the “nemesis of the fluctuations” and describe the way they have been inserted back within the LB formalism. The result is one of the most active sectors of current Lattice Boltzmann research.

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12

Succi, Sauro. Boltzmann’s Kinetic Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0002.

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Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic int

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13

Darrigol, Olivier. Atoms, Mechanics, and Probability. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.001.0001.

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One of the pillars of modern science, statistical mechanics, owes much to one man, the Austrian physicist Ludwig Boltzmann (1844–1906). As a result of his unusual working and writing styles, his enormous contribution remains little read and poorly understood. The purpose of this book is to make the Boltzmann corpus more accessible to physicists, philosophers, and historians, and so give it new life. The means are introductory biographical and historical materials, detailed and lucid summaries of every relevant publication, and a final chapter of critical synthesis. Special attention is given t

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14

Succi, Sauro. The Lattice Boltzmann Equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.001.0001.

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Over the past near three decades, the Lattice Boltzmann method has gained a prominent role as an efficient computational method for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales, from fully developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic subnuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this book presents a survey of the major developments w

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15

Darrigol, Olivier. Boltzmann’s Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0010.

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In this last chapter, the reader will find synthetic reflections on Boltzmann’s sources, on the basic components of his theory, and on the ways it was received. The basic components are arranged according to the natural order in which they occurred in Boltzmann’s theory making: constructive tools, chief constructions, crucial predictions, underlying concepts, bridges between different approaches. To fully understand his enterprise, one must embrace his theory as an entire whole organism. This is a difficult and time-consuming task, which this book is meant to ease. In the past, Boltzmann’s rea

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16

Succi, Sauro. Lattice Boltzmann Models without Underlying Boolean Microdynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0013.

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Chapter 12 showed how to circumvent two major stumbling blocks of the LGCA approach: statistical noise and exponential complexity of the collision rule. Yet, the ensuing LB still remains connected to low Reynolds flows, due to the low collisionality of the underlying LGCA rules. The high-viscosity barrier was broken just a few months later, when it was realized how to devise LB models top-down, i.e., based on the macroscopic hydrodynamic target, rather than bottom-up, from underlying microdynamics. Most importantly, besides breaking the low-Reynolds barrier, the top-down approach has proven ve

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17

Succi, Sauro. Lattice Boltzmann Models with Underlying Boolean Microdynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0012.

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This chapter takes a walk into the Jurassics of LBE, namely the earliest Lattice Boltzmann model that grew up out in response to the main drawbacks of the underlying LGCA. The earliest LBE was first proposed by G. McNamara and G. Zanetti in 1988, with the explicit intent of sidestepping the statistical noise problem plaguing its LGCA ancestor. The basic idea is simple: just replace the Boolean occupation Numbers with the corresponding ensemble-averaged population. The change in perspective is exactly the same as in Continuum Kinetic Theory (CKT); instead of tracking single Boolean molecules, o

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18

Darrigol, Olivier. The Analogical Turn (1884–1887). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0006.

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This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in r

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19

Myrvold, Wayne. Probabilities in Statistical Mechanics. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.26.

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This chapter reviews selected aspects of the terrain of discussion of the role of probabilities in statistical mechanics. Among the topics addressed are the reasons for introduction of probabilities into statistical mechanics, the status of the standard equilibrium distribution, and the question of interpretation of statistical mechanical probabilities. The chapter starts with a brief history of probabilities in physics and the evolution of statistical mechanics therefrom. The approaches of Boltzmann and Gibbs are presented, and then some approaches to justifying choice of probability measures

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20

Darrigol, Olivier. Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical Writings - an Exegesis. Oxford University Press, 2021.

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21

Gell-Mann, Murray, and Constantino Tsallis, eds. Nonextensive Entropy. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195159769.001.0001.

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A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure. Many of these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics and standard laws in a natural way. The book addresses the interdisciplinary applications of these ideas, and also on various phenomena that could possibly be quantitatively describable in terms of these ideas.

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22

Darrigol, Olivier. The Probabilistic Turn (1876–1884). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0005.

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This chapter deals with writings in which Boltzmann expressed the statistical nature of the entropy law and temporarily made the relation between entropy and combinatorial probability a basic constructive tool of his theory. In 1881, he discovered that this relation derived from what we now call the microcanonical distribution, and he approved Maxwell’s recent foundation of the equilibrium problem on the microcanonical ensemble. Boltzmann also kept working on problems he had tackled in earlier years. He proposed a new solution to the problem of specific heats, and he performed enormous calcula

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23

Darrigol, Olivier, and Jürgen Renn. The Emergence of Statistical Mechanics. Edited by Jed Z. Buchwald and Robert Fox. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199696253.013.26.

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This article traces the history of statistical mechanics, beginning with a discussion of mechanical models of thermal phenomena. In particular, it considers how several circumstances, including the establishment of thermodynamics in the mid-nineteenth century, led to a focus on the model of heat as a motion of particles. It then describes the concept of heat as fluid and the kinetic theory before turning to gas theory and how it served as a bridge between mechanics and thermodynamics. It also explores gases as particles in motion, the Maxwell–Boltzmann distribution, the problem of specific hea

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24

Morawetz, Klaus. Interacting Systems far from Equilibrium. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.001.0001.

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In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the int

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25

Swendsen, Robert H. An Introduction to Statistical Mechanics and Thermodynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.001.0001.

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This is a textbook on statistical mechanics and thermodynamics. It begins with the molecular nature of matter and the fact that we want to describe systems containing many (1020) particles. The first part of the book derives the entropy of the classical ideal gas using only classical statistical mechanics and Boltzmann’s analysis of multiple systems. The properties of this entropy are then expressed as postulates of thermodynamics in the second part of the book. From these postulates, the structure of thermodynamics is developed. Special features are systematic methods for deriving thermodynam

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26

Atoms, mechanics, and probability : Ludwig Boltzmann's statistico-mechanical writings - an exegesis - 1. edición. Oxford University Press, 2018.

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27

Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

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This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equ

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28

Clarke, Andrew. The Metabolic Theory of Ecology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199551668.003.0012.

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The model of West, Brown & Enquist (WBE) is built on the assumption that the metabolic rate of cells is determined by the architecture of the vascular network that supplies them with oxygen and nutrients. For a fractal-like network, and assuming that evolution has minimised cardiovascular costs, the WBE model predicts that s=metabolism should scale with mass with an exponent, b, of 0.75 at infinite size, and ~ 0.8 at realistic larger sizes. Scaling exponents ~ 0.75 for standard or resting metabolic rate are observed widely, but far from universally, including in some invertebrates with car

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29

Nolte, David D. The Tangled Tale of Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0006.

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This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability

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30

Rau, Jochen. Perfect Gas. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0006.

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The perfect gas is perhaps the most prominent application of statistical mechanics and for this reason merits a chapter of its own. This chapter briefly reviews the quantum theory of many identical particles, in particular the distinction between bosons and fermions, and then develops the general theory of the perfect quantum gas. It considers a number of limits and special cases: the classical limit; the Fermi gas at low temperature; the Bose gas at low temperature which undergoes Bose–Einstein condensation; as well as black-body radiation. For the latter we derive the Stefan–Boltzmann law, t

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31

Tiwari, Sandip. Information mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198759874.003.0001.

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Information is physical, so its manipulation through devices is subject to its own mechanics: the science and engineering of behavioral description, which is intermingled with classical, quantum and statistical mechanics principles. This chapter is a unification of these principles and physical laws with their implications for nanoscale. Ideas of state machines, Church-Turing thesis and its embodiment in various state machines, probabilities, Bayesian principles and entropy in its various forms (Shannon, Boltzmann, von Neumann, algorithmic) with an eye on the principle of maximum entropy as an

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32

Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and dis

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33

Henriksen, Niels E., and Flemming Y. Hansen. Theories of Molecular Reaction Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.001.0001.

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This book deals with a central topic at the interface of chemistry and physics—the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of physics, the book focuses on the theoretical framework for predicting the outcome of chemical reactions. The style is highly systematic with attention to basic concepts and clarity of presentation. Molecular reaction dynamics is about the detailed atomic-level description of chemical reactions. Based on quantum mechanics and statistical mechanics or, as an approximation, classical mechanics, the dynamics of

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34

Lemons, Don S., William R. Shanahan, and Louis J. Buchholtz. On the Trail of Blackbody Radiation. The MIT Press, 2022. http://dx.doi.org/10.7551/mitpress/14416.001.0001.

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An account of Max Planck's construction of his theory of blackbody radiation, summarizing the established physics on which he drew. In the last year of the nineteenth century, Max Planck constructed a theory of blackbody radiation—the radiation emitted and absorbed by nonreflective bodies in thermal equilibrium with one another—and his work ushered in the quantum revolution in physics. In this book, three physicists trace Planck's discovery. They follow the trail of Planck's thinking by constructing a textbook of sorts that summarizes the established physics on which he drew. By offering this

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35

Entropy and Energy: A Universal Competition (Interaction of Mechanics and Mathematics). Springer, 2005.

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