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|Title:||Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes|
|Authors:||Gorban, A. N.|
Kolokoltsov, V. N.
|Publisher:||EDP Sciences, Cambridge University Press (CUP)|
|Citation:||Mathematical Modelling of Natural Phenomena, 2015, 10 (5), pp. 16-46 (31)|
|Abstract:||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.|
|Rights:||Copyright © 2015, EDP Sciences, Cambridge University Press (CUP). Deposited with reference to the publisher’s open access archiving policy.|
|Description:||Mathematics Subject Classification: 80A30 / 60J25 / 60J60 / 60J75 / 82B40|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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