  We develop the stochastic approach to thermodynamics based on the stochastic
dynamics, which can be discrete (master equation) continuous (Fokker-Planck
equation), and on two assumptions concerning entropy. The first is the
definition of entropy itself and the second, the definition of entropy
production rate which is nonnegative and vanishes in thermodynamic equilibrium.
Based on these assumptions we study interacting systems with many degrees of
freedom in equilibrium or out of thermodynamic equilibrium, and how the
macroscopic laws are derived from the stochastic dynamics. These studies
include the quasi-equilibrium processes, the convexity of the equilibrium
surface, the monotonic time behavior of thermodynamic potentials, including
entropy, the bilinear form of the entropy production rate, the Onsager
coefficients and reciprocal relations, and the nonequilibrium steady states of
chemical reactions.
