Boltzmann and Poincaré Entropy, Boltzmann Extremals, and Hamilton–Jacobi Method for Non-Hamiltonian Situationстатья
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Дата последнего поиска статьи во внешних источниках: 20 апреля 2022 г.
Аннотация:In this paper, we prove the H-theorem for generalized chemical kinetics equations. Weconsider the following important physical examples of such a generalization: discrete models of quantumkinetic equations (Uehling–Uhlenbeck equations) and a quantum Markov process (quantum randomwalk). We prove that time means coincide with Boltzmann extremals for all such equations and forthe Liouville equation as well. This gives us an approach to select the action–angle variables in theHamilton–Jacobi method for the non-Hamiltonian situation. We propose a simple derivation of theHamilton–Jacobi equation from the Liouville equations in the finite-dimensional case.