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Journal articles on the topic 'Boltzmann statistics'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Mijatović, M., A. Jannussis, and A. Streclas. "Boltzmann statistics of quantum friction." Physics Letters A 122, no. 1 (1987): 31–35. http://dx.doi.org/10.1016/0375-9601(87)90770-5.

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2

Tsallis, Constantino. "Possible generalization of Boltzmann-Gibbs statistics." Journal of Statistical Physics 52, no. 1-2 (1988): 479–87. http://dx.doi.org/10.1007/bf01016429.

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3

Aghion, Erez, David A. Kessler, and Eli Barkai. "Infinite ergodic theory meets Boltzmann statistics." Chaos, Solitons & Fractals 138 (September 2020): 109890. http://dx.doi.org/10.1016/j.chaos.2020.109890.

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4

Saxena, R. K., A. M. Mathai, and H. J. Haubold. "Astrophysical thermonuclear functions for Boltzmann–Gibbs statistics and Tsallis statistics." Physica A: Statistical Mechanics and its Applications 344, no. 3-4 (2004): 649–56. http://dx.doi.org/10.1016/j.physa.2004.06.047.

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5

Iizuka, Jun, and Teruyuki Kitabayashi. "Fermi–Boltzmann statistics of neutrinos and relativistic effective degrees of freedom in the early universe." Modern Physics Letters A 30, no. 01 (2015): 1550003. http://dx.doi.org/10.1142/s0217732315500030.

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We investigate the effect of the presence of non-pure fermionic neutrinos on the relativistic effective degrees of freedom in the early universe. The statistics of neutrinos is transformed continuously from Fermi–Dirac to Maxwell–Boltzmann statistics. We find that the relativistic degrees of freedom decreases with the deviation from pure Fermi–Dirac statistics of neutrinos if there are constant and large lepton asymmetries. Additionally, we confirm that the change of the statistics of neutrinos from Fermi–Dirac to Maxwell–Boltzmann is not sufficient to cover the excess of the effective number

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6

Arkeryd, Leif, and Anne Nouri. "On a Boltzmann equation for Haldane statistics." Kinetic & Related Models 12, no. 2 (2019): 323–46. http://dx.doi.org/10.3934/krm.2019014.

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7

Bhaduri, R. K., R. S. Bhalerao, and M. V. N. Murthy. "Haldane exclusion statistics and the Boltzmann equation." Journal of Statistical Physics 82, no. 5-6 (1996): 1659–68. http://dx.doi.org/10.1007/bf02183398.

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8

Gehman, John D., Frances Separovic, Kun Lu, and Anil K. Mehta. "Boltzmann Statistics Rotational-Echo Double-Resonance Analysis." Journal of Physical Chemistry B 111, no. 27 (2007): 7802–11. http://dx.doi.org/10.1021/jp072504q.

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9

Kokowski, Michal. "Ladislas Natanson and Alfred Landé versus Planck's law, the Boltzmann-Planck- Natanson statistics and the Bose statistics." Studia Historiae Scientiarum 20 (September 13, 2021): 439–507. https://doi.org/10.4467/2543702XSHS.21.014.14045.

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The article describes the context and content of the November 1925 correspondence – so far overlooked by historians of physics – between Władysław (Ladislas) Natanson and Alfred Landé on Planck’s law and Bose statistics, and the effects of this interaction. The article publishes for the first time the transcription of two original letters in German and their translations into English.

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10

CANTCHEFF, MARCELO BOTTA, and JOSE A. C. NOGALES. "NON-BOLTZMANN STATISTICS AS AN ALTERNATIVE TO HOLOGRAPHY." International Journal of Modern Physics A 21, no. 15 (2006): 3127–31. http://dx.doi.org/10.1142/s0217751x06029399.

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An intriguing question related to black hole thermodynamics is that the entropy of a region shall scale as the area rather than the volume. In this essay we propose that the microscopical degrees of freedom contained in a given region of space, are statistically related in such a way that obey a nonstandard statistics, in which case an holographic hypothesis would not be needed. This could provide us with some insight about the nature of degrees of freedom of the geometry and/or the way in which gravitation plays a role in the statistic correlation between the degrees of freedom of a system.

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11

Alastuey, Angel, Françoise Cornu, and Asher Perez. "Virial expansions for quantum plasmas: Maxwell-Boltzmann statistics." Physical Review E 51, no. 3 (1995): 1725–44. http://dx.doi.org/10.1103/physreve.51.1725.

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12

Andrade, R. F. S. "Ising chain in the generalized Boltzmann-Gibbs statistics." Physica A: Statistical Mechanics and its Applications 175, no. 2 (1991): 285–92. http://dx.doi.org/10.1016/0378-4371(91)90407-4.

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13

Finkelstein, Alexei V., Azat Ya Badretdinov, and Alexander M. Gutin. "Why do protein architectures have boltzmann-like statistics?" Proteins: Structure, Function, and Genetics 23, no. 2 (1995): 142–50. http://dx.doi.org/10.1002/prot.340230204.

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14

Clarke, Will, Matthew J. Wolf, Alison Walker, and Giles Richardson. "Charge transport modelling of perovskite solar cells accounting for non-Boltzmann statistics in organic and highly-doped transport layers." Journal of Physics: Energy 5, no. 2 (2023): 025007. http://dx.doi.org/10.1088/2515-7655/acc4e9.

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Abstract We present a drift–diffusion model of a perovskite solar cell (PSC) in which carrier transport in the charge transport layers (TLs) is not based on the Boltzmann approximation to the Fermi–Dirac (FD) statistical distribution, in contrast to previously studied models. At sufficiently high carrier densities the Boltzmann approximation breaks down and the precise form of the density of states function (often assumed to be parabolic) has a significant influence on carrier transport. In particular, parabolic, Kane and Gaussian models of the density of states are discussed in depth and it i

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15

Kikuchi, Koji, and Hiroshi Akatsuka. "Reconsideration of Temperature Determined by the Excited-State Population Distribution of Hydrogen Atoms Based on Tsallis Entropy and Its Statistics in Hydrogen Plasma in Non-Equilibrium State." Entropy 25, no. 10 (2023): 1400. http://dx.doi.org/10.3390/e25101400.

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In non-equilibrium plasmas, the temperature cannot be uniquely determined unless the energy-distribution function is approximated as a Maxwell–Boltzmann distribution. To overcome this problem, we applied Tsallis statistics to determine the temperature with respect to the excited-state populations in non-equilibrium state hydrogen plasma, which enables the description of its entropy that obeys q-exponential population distribution in the non-equilibrium state. However, it is quite difficult to apply the q-exponential distribution because it is a self-consistent function that cannot be solved an

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16

Salakhutdinov, Ruslan, and Geoffrey Hinton. "An Efficient Learning Procedure for Deep Boltzmann Machines." Neural Computation 24, no. 8 (2012): 1967–2006. http://dx.doi.org/10.1162/neco_a_00311.

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We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent statistics are estimated using a variational approximation that tends to focus on a single mode, and data-independent statistics are estimated using persistent Markov chains. The use of two quite different techniques for estimating the two types of statistic that enter into the gradient of the log likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer p

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17

Cerreia-Vioglio, Simone, Fabio Maccheroni, Massimo Marinacci, and Aldo Rustichini. "Axiomatic tests for the Boltzmann distribution." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 1 (2021): 013406. http://dx.doi.org/10.1088/1742-5468/abd4ce.

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18

Dubois, François, and Pierre Lallemand. "Towards higher order lattice Boltzmann schemes." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 06 (2009): P06006. http://dx.doi.org/10.1088/1742-5468/2009/06/p06006.

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19

Hao, Junyao. "The Boltzmann distribution in gravity field." Theoretical and Natural Science 10, no. 1 (2023): 296–303. http://dx.doi.org/10.54254/2753-8818/10/20230366.

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The air is comprised of innumerable particles. In the atmosphere, the particles are mostly gas molecules, including nitrogen, oxygen, and hydrogen, extending in the air in a gravitational field caused by Earth. With thermal statistics, there are methods to calculate and observe some microscopic properties of this group of particles. This essay aims to disclose the density distribution of gas particles in the air from different altitudes and at different speeds. All the calculations have proceeded on the approximately ideal circumstance with some corrections. The calculation and observation met

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20

Gajewski, Herbert, and Konarad Gröger. "Semiconductor Equations for variable Mobilities Based on Boltzmann Statistics or Fermi-Dirac Statistics." Mathematische Nachrichten 140, no. 1 (1989): 7–36. http://dx.doi.org/10.1002/mana.19891400102.

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21

Saiz, A. "Boltzmann power laws." Physica A: Statistical Mechanics and its Applications 389, no. 2 (2010): 225–36. http://dx.doi.org/10.1016/j.physa.2009.09.032.

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22

Abdulsalam, Azwar, and Joseph G. Makin. "Exponential-Family Harmoniums with Neural Sufficient Statistics." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 15 (2025): 15284–92. https://doi.org/10.1609/aaai.v39i15.33677.

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Exponential-family harmoniums (EFHs) generalize the restricted Boltzmann machine beyond Bernoulli random variables to other exponential families. Here we show how to extend the EFH beyond standard exponential families (Poisson, Gaussian, etc.), by allowing the sufficient statistics for the hidden units to be arbitrary functions of the observed data, parameterized by deep neural networks. This rules out the standard sampling scheme, block Gibbs sampling, so we replace it with a form of Langevin dynamics within Gibbs, inspired by a recent method for training Gaussian restricted Boltzmann machine

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23

Bauer, Wolfgang Rudolf. "How geometrically frustrated systems challenge our notion of thermodynamics." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 3 (2022): 033208. http://dx.doi.org/10.1088/1742-5468/ac59b5.

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Abstract Although Boltzmann’s definition of entropy and temperature are widely accepted, we will show scenarios which apparently are inconsistent with our normal notion of thermodynamics. We focus on generic geometrically frustrated systems (GFSs), which stay at constant negative Boltzmann temperatures, independent from their energetic state. Two weakly coupled GFSs at same temperature exhibit, in accordance with energy conservation, the same probability for all energetic combinations. Heat flow from a hot GFS to a cooler GFS or an ideal gas increases Boltzmann entropy of the combined system,

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24

de Almeida, N. G. "Formal equivalence between Tsallis and extended Boltzmann–Gibbs statistics." Physica A: Statistical Mechanics and its Applications 387, no. 12 (2008): 2745–49. http://dx.doi.org/10.1016/j.physa.2008.01.066.

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25

Niven, Robert K. "Exact Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac statistics." Physics Letters A 342, no. 4 (2005): 286–93. http://dx.doi.org/10.1016/j.physleta.2005.05.063.

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26

Bach, Alexander. "The Maxwell-Boltzmann distribution derived from Bose-Einstein statistics." Physics Letters A 134, no. 1 (1988): 1–3. http://dx.doi.org/10.1016/0375-9601(88)90535-x.

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27

Cohen, E. G. D. "Boltzmann and Einstein: Statistics and dynamics — An unsolved problem." Pramana 64, no. 5 (2005): 635–43. http://dx.doi.org/10.1007/bf02704573.

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28

Belgacem, Chokri Hadj. "Comparative study between exponential Boltzmann and Lambert Boltzmann distributions for heat capacity calculation." International Journal of Modern Physics B 33, no. 14 (2019): 1950140. http://dx.doi.org/10.1142/s0217979219501406.

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The Stirling’s estimation to [Formula: see text](N!) is typically introduced to students as a step in the derivation of the statistical expression for the heat capacity. However, naïve application of this estimation leads to wrong conclusions. In this paper, firstly, the heat capacity of some semiconductor compounds was calculated using exponential Boltzmann distribution and compared with experimental data. It has shown a disagreement between experimental results and those calculated. Secondly, by applying the more exact Stirling formula, an analytical formulation of Boltzmann statistics using

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29

BENEDETTO, D., M. PULVIRENTI, F. CASTELLA, and R. ESPOSITO. "ON THE WEAK-COUPLING LIMIT FOR BOSONS AND FERMIONS." Mathematical Models and Methods in Applied Sciences 15, no. 12 (2005): 1811–43. http://dx.doi.org/10.1142/s0218202505000984.

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In this paper we consider a large system of bosons or fermions. We start with an initial datum which is compatible with the Bose–Einstein, respectively Fermi–Dirac, statistics. We let the system of interacting particles evolve in a weak-coupling regime. We show that, in the limit, and up to the second order in the potential, the perturbative expansion expressing the value of the one-particle Wigner function at time t, agrees with the analogous expansion for the solution to the Uehling–Uhlenbeck equation. This paper follows the same spirit as the companion work,2 where the authors investigated

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30

Tao, Yong. "Self-referential Boltzmann machine." Physica A: Statistical Mechanics and its Applications 545 (May 2020): 123775. http://dx.doi.org/10.1016/j.physa.2019.123775.

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31

Mellet, Antoine, and Benoı̂t Perthame. "L1 contraction property for a Boltzmann equation with Pauli statistics." Comptes Rendus Mathematique 335, no. 4 (2002): 337–40. http://dx.doi.org/10.1016/s1631-073x(02)02495-0.

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32

Gil-Villegas, A., O. Obregón, and J. Torres-Arenas. "Computer simulation of effective potentials for generalized Boltzmann-Gibbs statistics." Journal of Molecular Liquids 248 (December 2017): 364–69. http://dx.doi.org/10.1016/j.molliq.2017.10.027.

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33

Bach, Alexander. "Indistinguishability or distinguishability of the particles of Maxwell-Boltzmann statistics." Physics Letters A 125, no. 9 (1987): 447–50. http://dx.doi.org/10.1016/0375-9601(87)90182-4.

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34

Bach, A. "Why Are Independent Bosons Distributed According to Maxwell-Boltzmann Statistics?" Europhysics Letters (EPL) 14, no. 5 (1991): 391–96. http://dx.doi.org/10.1209/0295-5075/14/5/001.

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35

Kakorin, S. "Revision of Boltzmann statistics for a finite number of particles." American Journal of Physics 77, no. 1 (2009): 48–53. http://dx.doi.org/10.1119/1.2967703.

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36

Melchior, Jan, Nan Wang, and Laurenz Wiskott. "Gaussian-binary restricted Boltzmann machines for modeling natural image statistics." PLOS ONE 12, no. 2 (2017): e0171015. http://dx.doi.org/10.1371/journal.pone.0171015.

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37

Huber, Thomas, and Andrew E. Torda. "Protein fold recognition without Boltzmann statistics or explicit physical basis." Protein Science 7, no. 1 (1998): 142–49. http://dx.doi.org/10.1002/pro.5560070115.

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38

Schuster, Peter. "Boltzmann, atomism, evolution, and statistics: Continuity versus discreteness in biology." Complexity 11, no. 6 (2006): 9–11. http://dx.doi.org/10.1002/cplx.20144.

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39

Li, Bao-Chun, Guo-Xing Zhang, and Yuan-Yuan Guo. "Transverse Momentum Spectra ofKS0andK*0at Midrapidity ind+ Au, Cu + Cu, andp+pCollisions atsNN=200 GeV." Advances in High Energy Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/684950.

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We analyze transverse momentum spectra ofKS0andK*0at midrapidity ind+ Au, Cu + Cu, andp+pcollisions atsNN=200 GeV in the formworks of Tsallis statistics and Boltzmann statistics, respectively. Both of them can describe the transverse momentum spectra and extract the thermodynamics parameters of matter evolution in the collisions. The parameters are helpful for us to understand the thermodynamics factors of the particle production.

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40

Valdivieso Colmenares, Miguel Alfonso, and José Daniel Muñoz Castaño. "Numerical comparison of 1D quantum lattice Boltzmann models." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 06 (2009): P06004. http://dx.doi.org/10.1088/1742-5468/2009/06/p06004.

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41

Tramel, Eric W., Angélique Drémeau, and Florent Krzakala. "Approximate message passing with restricted Boltzmann machine priors." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 7 (2016): 073401. http://dx.doi.org/10.1088/1742-5468/2016/07/073401.

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42

Walker, A. L., D. L. Curry, and H. B. Fannin. "Comparison of Methodologies for the Determination of Excitation Temperatures of Plasma Support Gases." Applied Spectroscopy 48, no. 3 (1994): 333–37. http://dx.doi.org/10.1366/0003702944028290.

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Methodologies for the determination of excitation temperatures for the argon support gas in six inductively coupled plasma systems are compared. These methods include a Boltzmann plot, partial Boltzmann plots, a polynomial fit, and a Fermi-Dirac model. The temperature(s) and fitting statistics are reported for each method. Additionally, the theoretical basis for each method is briefly reviewed. All these methods, with the exception of the first and last, yield multiple excitation temperatures; however, the Fermi-Dirac model more closely models the observed population distribution of excited el

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43

Yang, Jaw-Yen, Bagus Putra Muljadi, Zhi-Hui Li, and Han-Xin Zhang. "A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics." Communications in Computational Physics 14, no. 1 (2013): 242–64. http://dx.doi.org/10.4208/cicp.290112.030812a.

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AbstractAn accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of the discretized velocity distribution function in physical space and time. The method

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44

Ishihara, Masamichi. "Application of optimization method to the x4 model in the Tsallis nonextensive statistics." International Journal of Modern Physics B 29, no. 01 (2014): 1450234. http://dx.doi.org/10.1142/s0217979214502348.

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We study the effects of the environment described by the Tsallis nonextensive statistics on physical quantities using an optimization method in the case of small deviation from the Boltzmann–Gibbs statistics. The x4 model is used and the density operator is restricted to be a Gaussian form. The variational parameter is the frequency Ω of a harmonic oscillator in the optimization method. We obtain an approximate expression of free energy and of the expectation value of βmΩ2 x2/2, where β is the inverse of the temperature T and m is the mass. The optimized frequency is estimated numerically. The

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45

Moradpour, Hooman, Mohsen Javaherian, Ebrahim Namvar, and Amir Hadi Ziaie. "Gamow Temperature in Tsallis and Kaniadakis Statistics." Entropy 24, no. 6 (2022): 797. http://dx.doi.org/10.3390/e24060797.

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Relying on the quantum tunnelling concept and Maxwell–Boltzmann–Gibbs statistics, Gamow shows that the star-burning process happens at temperatures comparable to a critical value, called the Gamow temperature (T) and less than the prediction of the classical framework. In order to highlight the role of the equipartition theorem in the Gamow argument, a thermal length scale is defined, and then the effects of non-extensivity on the Gamow temperature have been investigated by focusing on the Tsallis and Kaniadakis statistics. The results attest that while the Gamow temperature decreases in the f

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46

SHEVCHENKO, VLADIMIR. "INFINITE STATISTICS, SYMMETRY BREAKING AND COMBINATORIAL HIERARCHY." Modern Physics Letters A 24, no. 18 (2009): 1425–35. http://dx.doi.org/10.1142/s0217732309030825.

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The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments, it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarc

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47

Yang, Jaw-Yen, Li-Hsin Hung, and Yao-Tien Kuo. "Semiclassical Lattice Boltzmann Simulations of Rarefied Circular Pipe Flows." Communications in Computational Physics 10, no. 2 (2011): 405–21. http://dx.doi.org/10.4208/cicp.060210.270810a.

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AbstractComputations of microscopic circular pipe flow in a rarefied quantum gas are presented using a semiclassical axisymmetric lattice Boltzmann method. The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations in two-dimensional rectangular coordinates onto the tensor Hermite polynomials using moment expansion method and then the forcing strategy of Halliday et al. [Phys. Rev. E., 64 (2001), 011208] is adopted by adding forcing terms into the resulting microdynamic evolution equation. The determination of the forcing terms is dictated by yielding the

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48

Muljadi, Bagus Putra, and Jaw-Yen Yang. "Simulation of shock wave diffraction by a square cylinder in gases of arbitrary statistics using a semiclassical Boltzmann–Bhatnagar–Gross–Krook equation solver." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2139 (2011): 651–70. http://dx.doi.org/10.1098/rspa.2011.0275.

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The unsteady shock wave diffraction by a square cylinder in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the discrete ordinate method for discretizing the velocity space of the distribution function and high-resolution method is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is employed. The complete diffraction patterns including regular reflection, tripl

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49

Kleinert, H., and X. J. Chen. "Boltzmann distribution and market temperature." Physica A: Statistical Mechanics and its Applications 383, no. 2 (2007): 513–18. http://dx.doi.org/10.1016/j.physa.2007.04.101.

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50

GOLDSMAN, NEIL, and CHUNG-KUANG HUANG. "SELF-CONSISTENT MODELING OF MOSFET QUANTUM EFFECTS BY SOLVING THE SCHRÖDINGER AND BOLTZMANN SYSTEM OF EQUATIONS." International Journal of High Speed Electronics and Systems 13, no. 03 (2003): 803–22. http://dx.doi.org/10.1142/s0129156403002034.

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A new method for investigating quantum confinement effects in MOSFETs is presented. The method is based on the numerical solution of the Schrödinger and Boltzmann system of equations. A quantum Boltzmann equation is developed by replacing the classical potential with a quantum potential. The technique naturally accounts for highly nonequilibrium effects including velocity overshoot. The subbands are calculated and then populated using nonequilibrium statistics. Modeling results show the electron concentration and electron current density peaks shifted away from the interface. Calculations show

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