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On entropy-type functionals arising in stochastic chemical kinetics related to the concentration of the invariant measure and playing the role of Lyapunov functions in the dynamics of quasiaverages

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Abstract

This paper studies the relationship between the Lyapunov function of a macrosystem whose dynamics is governed by the laws of stochastic chemical kinetics and the invariant measure of this macrosystem arising at large times. A necessary and sufficient condition for the reduction of the search problem for the equilibrium of the macrosystem (the most probable macrostate of the invariant measure of this macrosystem) to an entropy-linear programming problem is given.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Moscow, Russia

    A. V. Gasnikov & E. V. Gasnikova

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  1. A. V. Gasnikov
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  2. E. V. Gasnikova
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Correspondence to A. V. Gasnikov.

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Original Russian Text © A. V. Gasnikov, E. V. Gasnikova, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 6, pp. 819–827.

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Gasnikov, A.V., Gasnikova, E.V. On entropy-type functionals arising in stochastic chemical kinetics related to the concentration of the invariant measure and playing the role of Lyapunov functions in the dynamics of quasiaverages. Math Notes 94, 854–861 (2013). https://doi.org/10.1134/S0001434613110229

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  • DOI: https://doi.org/10.1134/S0001434613110229

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