TY - JOUR

T1 - Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes

AU - Gorban, A. N.

AU - Kolokoltsov, V. N.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - Entropy

KW - Lyapunov functional

KW - Markov process

KW - Nonlinear kinetics

KW - Quasi steady state

KW - Quasiequilibrium

UR - http://www.scopus.com/inward/record.url?scp=84940643060&partnerID=8YFLogxK

U2 - 10.1051/mmnp/201510503

DO - 10.1051/mmnp/201510503

M3 - Article

AN - SCOPUS:84940643060

VL - 10

SP - 16

EP - 46

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

IS - 5

ER -