Reversibility, Heat Dissipation, and the Importance of the Thermal Environment in Stochastic Models of Nonequilibrium Steady States

We examine stochastic processes that are used to model nonequilibrium processes (e.g., pulling RNA or dragging colloids) and so deliberately violate detailed balance. We argue that by combining an information-theoretic measure of irreversibility with nonequilibrium work theorems, the thermal physics implied by abstract dynamics can be determined. This measure is bounded above by thermodynamic entropy production and so may quantify how well a stochastic dynamics models reality. We also use our findings to critique various modeling approaches and notions arising in steady-state thermodynamics.

Figure 1

Biased diffusion arising from the local or generalized detailed balance principles applied to hard-core particles in a one-dimensional linear potential gradient under (a) open and (b) periodic boundary conditions.

Figure 2

Comparison of trajectories generated by the forward and reverse processes. Forward trajectories of length $T$ are generated, at which point all velocities (shown as short arrows) are flipped, and the reverse dynamics started. The heaviness of the lines indicates the probability of the trajectories in each ensemble. The central trajectory appears with the same probability in both ensembles, whereas the outer trajectories appear with different probabilities, thus indicating an irreversible dynamics.