  The nonlinear Markov processes are the 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.
