Abstract
We introduce an infinite particle system dynamics, which includes stochastic chemical kinetics models, the classical Kac model and free space movement. We study energy redistribution between two energy types (kinetic and chemical) in different time scales, similar to energy redistribution in the living cell. One example is considered in great detail, where the model provides main formulas of chemical thermodynamics.
Similar content being viewed by others
References
L. Arnold M. Theodosopulu (1980) ArticleTitleDeterministic limit of the stochastic model of chemical reactions with diffusion Adv. Appl. Prob. 12 367–379
M. Bramson and J. Lebowitz. Spatial structure in low dimensions for diffusion limited two-particle reactions. Ann. Appl. Prob. (2001).
R. Dobrushin (1956) ArticleTitleOn the Poisson law for the distribution of particles in space Ukrainian Math. J. 8 IssueID2 130–134
Fayolle G., Malyshev V., Pirogov S. (2004). Stochastic chemical kinetics with energy parameters. Rapports de Recherche, INRIA, No. 5008, 2003. To appear in “Trends in Mathematics: Mathematics and Computer Science”, v. 3, Birkhauser,
C. Gadgil, Chang-Hyeong Lee and H. Othmer, A stochastic analysis of first-order reaction networks. Preprint, 2003.
M. Kac, Probability and Related Topics in Physical Sciences (Interscience Publishers, 1958).
J. Keizer (1987) Statistical Thermodynamics of Nonequilibrium Processes Springer Berlin.
P. Kotelenez (1986) ArticleTitleLaw of large numbers and central limit theorem for linear chemical reaction with diffusion Ann. Prob. 14 173–193
L. Landay (1976) Lifshitz. Course of Theoretical Physics, v. 5 Statistical Physics Moscow. 584
J. Lebowitz Ch. Maes (2003) Entropy–a Dialog In. “Entropy” Princeton Univ Press Princeton. 269–276
M.A. Leontovich (1935) ArticleTitleMain equations of kinetical theory of gases from the random processes point of view J. Experim. Theor. Physics. 5 IssueID3–4 211–231
Th. Ligget (1985) Interacting Particle Systems Springer Berlin 496
C. Maes K. Netocny M. Verschuere (2003) ArticleTitleHeat conduction networks, J Stat. Phys. 111 1219–1244 Occurrence Handle10.1023/A:1023004300229
Ch. Maes M. Wieren Particlevan (2003) ArticleTitleA Markov model for kinesin JSP. 112 IssueID1/2 329–335
Malyshev V., Minlos R. (1995). Linear infinite-particle operators. AMS Translations Math. Monographs. 143
Malyshev V., Pirogov S., Rybko A. (2004). Random walks and chemical networks. Moscow Math. J. 2
A. De Masi P. Ferrari J.L. Lebowitz (1986) ArticleTitleReaction–diffusion equations for interacting particle systems J. Stat. Phys. 44 IssueID3/4 589–644 Occurrence Handle10.1007/BF01011311
D. McQuarrie (1967) ArticleTitleStochastic approach to chemical kinetics J. Appl. Prob. 4 413–478
H. Othmer, Analysis of complex reaction networks. University of Minnesota preprint, Minneapolis, December 9, 2003.
R. F. Streater, Statistical Dynamics. Imperial College Press, 1995.
J. Tuszynski, M. Kurzynski, Introduction to molecular biophysics CRC Press, 2003.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Malyshev, V.A. Microscopic Models for Chemical Thermodynamics. J Stat Phys 119, 997–1026 (2005). https://doi.org/10.1007/s10955-005-4408-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-005-4408-z