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Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes

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journal contribution
posted on 21.03.2017, 09:59 by A. N. Gorban, V. N. Kolokoltsov
The nonlinear Markov processes are measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.

History

Citation

Mathematical Modelling of Natural Phenomena, 2015, 10 (5), pp. 16-46 (31)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

VoR (Version of Record)

Published in

Mathematical Modelling of Natural Phenomena

Publisher

EDP Sciences, Cambridge University Press (CUP)

issn

0973-5348

eissn

1760-6101

Copyright date

2015

Available date

21/03/2017

Publisher version

http://www.mmnp-journal.org/articles/mmnp/abs/2015/05/mmnp201510p16/mmnp201510p16.html

Notes

Mathematics Subject Classification: 80A30 / 60J25 / 60J60 / 60J75 / 82B40

Language

en