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**1 - 5**of**5**### Entropy Principle and Recent Results in Non-Equilibrium Theories

- ENTROPY
, 2014

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### Article Contact Geometry of Mesoscopic Thermodynamics and Dynamics

, 2014

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### Three Waves of Chemical Dynamics

"... Abstract. Three epochs in development of chemical dynamics are presented. We try to un-derstand the modern research programs in the light of classical works. The first Nobel Prize in Chemistry was awarded in 1901 to Jacobus H. van’t Hoff “in recognition of the extraordinary services he has rendered ..."

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Abstract. Three epochs in development of chemical dynamics are presented. We try to un-derstand the modern research programs in the light of classical works. The first Nobel Prize in Chemistry was awarded in 1901 to Jacobus H. van’t Hoff “in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions”. This award celebrated the end of the first epoch in chemical dynamics, discovery of the main laws. This epoch begun in 1864 when Waage and Guldberg published their first paper about Mass Action Law [42]. Van’t Hoff rediscovered this law independently in 1877. In 1984 the first book about chemical dynamics was published, van’t Hoff’s “Études de Dynamique chimique [40]”, in which he proposed the ‘natural ’ classification of simple reactions according to the number of molecules that are simultaneously participate in the reaction. Despite his announcement, “I have not accepted a concept of mass action law as a theoretical foundation”, van’t Hoff did the next step to the development of the same law. He also studied the relations between kinetics and thermodynamics and found the temperature dependence of equilibrium constant (the van’t Hoff equation). In particular, he proved the “principle of mobile equilibrium”: the equilibrium in a system tends to shift in such a direction as to oppose the temperature change which is imposed upon the system. This principle was later on generalized

### Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes

"... Abstract. The nonlinear Markov processes are measure-valued dynamical systems which pre-serve 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, ..."

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Abstract. The nonlinear Markov processes are measure-valued dynamical systems which pre-serve 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.