  We investigate the nonequilibrium stationary states of systems consisting of
chemical reactions among molecules of several chemical species. To this end we
introduce and develop a stochastic formulation of nonequilibrium thermodynamics
of chemical reaction systems based on a master equation defined on the space of
microscopic chemical states, and on appropriate definitions of entropy and
entropy production, The system is in contact with a heat reservoir, and is
placed out of equilibrium by the contact with particle reservoirs. In our
approach, the fluxes of various types, such as the heat and particle fluxes,
play a fundamental role in characterizing the nonequilibrium chemical state. We
show that the rate of entropy production in the stationary nonequilibrium state
is a bilinear form in the affinities and the fluxes of reaction, which are
expressed in terms of rate constants and transition rates, respectively. We
also show how the description in terms of microscopic states can be reduced to
a description in terms of the numbers of particles of each species, from which
follows the chemical master equation. As an example, we calculate the rate of
entropy production of the first and second Schl\"ogl reaction models.
