Fluctuation-Dissipation Theorem and Detailed Balance in Langevin Systems (original) (raw)

Equilibrium is characterized by its fundamental properties such as the fluctuation-dissipation theorem, the detailed balance, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin systems with microscopic reversibility. In the presence of velocity-dependent forces breaking the microscopic reversibility, we prove that the fluctuation-dissipation theorem and the detailed balance mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a nonequilibrium steady state with velocity-dependent forces may share some equilibrium properties but not all of them, in contrast that it can not share any of them without velocity-dependent forces. Our results are illustrated with a few example systems.