Detailed fluctuation theorem for mesoscopic modeling

The detailed fluctuation theorem is derived. The basic assumptions are phase space incompressibility (Liouville’s theorem) and time reversibility on the microscopic level. The theorem relates the conditional probability to end up in a mesoscopic state [Formula presented] at time [Formula presented], starting from [Formula presented] at time [Formula presented], to the time-reversed process. The ratio of these two probability densities is related to the entropy difference of the two mesoscopic states. The fluctuation theorem remains valid even far from equilibrium as long as the local equilibrium condition is obeyed. It is shown that the theorem imposes constraints on the form mesoscopic equations can take. For stochastic differential equations a generalized kinetic form is derived. The fluctuation theorem can be used to derive thermodynamically consistent simulation techniques. At the end of this paper the relation with the GENERIC formalism is discussed.