1209.3081 (Hao Ge)

Time reversibility and nonequilibrium thermodynamics of second-order
stochastic systems with inertia    [PDF]

Hao Ge

We rigorously investigate the condition of time reversibility as well as detailed balancing for the second-order stochastic process with inertia. We show that the time-reversibility could not even guarantee the steady state to be at thermal equilibrium. The real thermal equilibrium demands the other condition of detailed balance regarding the interaction between the internal system and its contacting reservoir, i.e. agreeing with the Maxwell-Boltzmann velocity distribution. We show that frictional force naturally emerges as the only odd term of the force at thermal equilibrium when both conditions of detailed balance are satisfied. The two conditions correspond to two different previously reported entropy production rates respectively, followed by two equations of entropy balance. When the external force is only dependent on the spatial coordinates, the two entropy balance equations become the same. The entropy production rates of the second-order stochastic process and its corresponding overdamped first-order process without inertia are only consistent if there is no temperature gradient. In the presence of temperature gradient, we prove that the former must be at nonequilibrium (time-irreversible), while the latter could still possibly be time-reversible.

View original: http://arxiv.org/abs/1209.3081