  In stochastic thermodynamics, the entropy production of a thermodynamic
system is defined by the irreversibility measured by the logarithm of the ratio
of the path probabilities in the forward and reverse processes. We derive the
relation between the irreversibility and the entropy production starting from
the deterministic equations of motion of the whole system consisting of a
physical system and a surrounding thermal environment. The physical system is
driven by a nonconservative force. The derivation assumes the Markov
approximation that the environmental degrees of freedom equilibrate
instantaneously. Our approach concerns the irreversibility of the whole system
not only the irreversibility of the physical system only. This approach
provides a guideline for the choice of the proper reverse process to a given
forward process. We demonstrate our idea with an example of a charged particle
in the presence of a time-varying magnetic field.
