Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes

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...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2015-01, Vol.10 (5), p.16-46
Main Authors: Gorban, A. N., Kolokoltsov, V. N.
Format: Article
Language:English
Subjects:
60J25
60J60
60J75
80A30
82B40
Entropy
Free energy
Heredity
Inheritances
Kinetic equations
Lyapunov functional
Markov analysis
Markov chains
Markov process
Nonlinear analysis
Nonlinear equations
nonlinear kinetics
quasi steady state
quasiequilibrium
Thermodynamic properties
Thermodynamics
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Summary: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.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/201510503