×

Inverse relationship between diffusion coefficient and mass for a free particle system: approach by using maximum caliber principle and Monte Carlo simulations. (English) Zbl 07880335


MSC:

37-XX Dynamical systems and ergodic theory
34-XX Ordinary differential equations
Full Text: DOI

References:

[1] Jaynes, E. T., Information theory and statistical mechanics, Phys. Rev., 106, 620-630, 1957 · Zbl 0084.43701 · doi:10.1103/PhysRev.106.620
[2] Jaynes, E. T., Information theory and statistical mechanics II, Phys. Rev., 108, 171-180, 1957 · Zbl 0084.43701 · doi:10.1103/PhysRev.108.171
[3] Chib, S., Markov chain Monte Carlo methods: Computation and inference, Handb. Econom., 5, 3569-3649, 2001 · doi:10.1016/S1573-4412(01)05010-3
[4] Davies, M. E., Nonlinear noise reduction through Monte Carlo sampling, Chaos, 8, 775, 1998 · Zbl 1039.62502 · doi:10.1063/1.166363
[5] Huang, K., Statistical Mechanics, 1987, Wiley · Zbl 1041.82500
[6] Soto, R., Kinetic Theory and Transport Phenomena, 2016, Oxford Master Series in Physics · Zbl 1374.82002
[7] Einstein, A., Uber die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen, Ann. Phys., 322, 8, 549-560, 1905 · JFM 36.0975.01 · doi:10.1002/andp.19053220806
[8] von Smoluchowski, M., Zur kinetischen theorie der brownschen molekularbewegung und der suspensionen, Ann. Phys., 326, 14, 756-780, 1906 · JFM 37.0814.03 · doi:10.1002/andp.19063261405
[9] González, D.; Diaz, D.; Davis, S., Continuity equation for probability as a requirement of inference over paths, Eur. Phys. J. B, 89, 214, 2016 · doi:10.1140/epjb/e2016-70307-0
[10] Hastings, W. K., Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109, 1970 · Zbl 0219.65008 · doi:10.1093/biomet/57.1.97
[11] Tapias, D.; Sanders, D. P.; Altmann, E. G., Monte Carlo sampling in diffusive dynamical systems, Chaos, 28, 053113, 2018 · Zbl 1391.37056 · doi:10.1063/1.5025627
[12] González, D.; Davis, S.; Gutiérrez, G., Newtonian dynamics from the principle of maximum caliber, Found. Phys., 44, 923, 2014 · Zbl 1302.70003 · doi:10.1007/s10701-014-9819-8
[13] Davis, S.; Gonzalez, D., Hamiltonian formalism and path entropy maximization, J. Phys. A: Math. Theor., 48, 42, 425003, 2015 · Zbl 1330.82040 · doi:10.1088/1751-8113/48/42/425003
[14] González, D.; Davis, S., The maximum caliber principle applied to continuous systems, J. Phys.: Conf. Ser., 720, 012006, 2016 · doi:10.1088/1742-6596/720/1/012006
[15] Jaynes, E. T., The minimum entropy production principle, Ann. Rev. Phys. Chem., 31, 579-601, 1980 · doi:10.1146/annurev.pc.31.100180.003051
[16] Jaynes, E. T., On the rationale of maximum-entropy methods, Proc. IEEE, 10, 939-952, 1982 · doi:10.1109/PROC.1982.12425
[17] Attard, P., Thermodynamics and Statistical Mechanics: Equilibrium by Entropy Maximisation, 2002, Academic Press
[18] Caticha, A.
[19] Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 2005, World Scientific Publishing
[20] Feynman, R. P.; Hibbs, A. R., Quantum Mechanics and Path Integrals, 2005, McGraw-Hill: McGraw-Hill, New York · Zbl 0176.54902
[21] Kac, M., On distributions of certain Wiener functionals, Trans. Am. Math. Soc., 65, 1-13, 1949 · Zbl 0032.03501 · doi:10.1090/S0002-9947-1949-0027960-X
[22] Feynman, R. P.; Brown, L., Feynman’s Thesis: A New Approach to Quantum Theory, 2005, World Scientific Publishing Co. Pte. Ltd. · Zbl 1122.81007
[23] Machlup, S.; Onsager, L., Fluctuations and irreversible process. II. Systems with kinetic energy, Phys. Rev., 91, 1512, 1953 · Zbl 0053.15107 · doi:10.1103/PhysRev.91.1512
[24] Gonzalez, D.; Davis, S.; Curilef, S., Solving equations of motion by using Monte Carlo metropolis: Novel method via random paths sampling and the maximum caliber principle, Entropy, 22, 9, 916, 2020 · doi:10.3390/e22090916
[25] Purcell, E. M., Electricidad y Magnetismo, 1988, Berkeley Physics Course
[26] Gonzalez, D.; Davis, S., Liouville’s theorem from the principle of maximum caliber in phase space, AIP Conf. Proc., 1757, 020003, 2016 · doi:10.1063/1.4959044
[27] Davis, S.; Gutiérrez, G., Conjugate variables in continuous maximum-entropy inference, Phys. Rev. E, 86, 051136, 2012 · doi:10.1103/PhysRevE.86.051136
[28] Haken, H., A new access to path integrals and Fokker-Planck equations via the maximum caliber principle, Z. Phys. B: Condens. Matter, 63, 505-510, 1986 · doi:10.1007/BF01726199
[29] Zwanzig, R., Nonequilibrium Statistical Mechanics, 2001, Oxford University Press · Zbl 1267.82001
[30] Nelson, E., Derivation of the Schrödinger equation from Newtonian mechanics, Phys. Rev., 150, 1079-1085, 1966 · doi:10.1103/PhysRev.150.1079
[31] Caticha, A., Entropic dynamics, Entropy, 17, 6110-6128, 2015 · doi:10.3390/e17096110
[32] Pessoa, P.; Costa, F. X.; Caticha, A., Entropic dynamics on Gibbs statistical manifolds, Entropy, 23, 5, 494, 2021 · doi:10.3390/e23050494
[33] Parker, M. C.; Jeynes, C., Maximum entropy (most likely) double helical and double logarithmic spiral trajectories in space-time, Sci. Rep., 9, 10779, 2019 · doi:10.1038/s41598-019-46765-w
[34] Cordoba, P.; Isidro, J.; Perea, M., Emergence from irreversibility, J. Phys.: Conf. Ser., 442, 012033, 2013 · doi:10.1088/1742-6596/442/1/012033
[35] Abad, L. V., Principles of classical statistical mechanics: A perspective from the notion of complementarity, Ann. Phys., 327, 1682-1693, 2012 · Zbl 1243.82007 · doi:10.1016/j.aop.2012.03.002
[36] Davis, S.; Gonzalez, D.; Gutierrez, G., Probabilistic inference for dynamical systems, Entropy, 20, 9, 696, 2018 · doi:10.3390/e20090696
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.