  We reconsider a well-known relationship between the fluctuation theorem and
the second law of thermodynamics by evaluating a probability measure-valued
process. In order to establish a bridge between microscopic and macroscopic
behaviors, we consider the thermodynamic limit of a stochastic dynamical system
following the fundamental procedure often used in statistical mechanics. The
thermodynamic path characterizing a macroscopic dynamical behavior can be
formulated as an infimum of the action functional for the probability
measure-valued process. In our formulation, the second law of thermodynamics
can be derived by symmetry of the action functional, which is generated from
the fluctuation theorem. We find that our formulation not only confirms that
the ordinary Jarzynski equality in the thermodynamic limit can be rederived,
but also enables us to establish a nontrivial nonequilibrium work relation for
metastable states.
