Time arrow in open-boundary one-dimensional stochastic dynamics

Abstract

We consider the finite-timestep stochastic dynamics of a single particle confined in one dimension, while the system has a nonuniform temperature profile. Under the open-boundary condition, one cannot observe any net probability current in the nonequilibrium steady state (NESS). On the other hand, the nonequilibrium nature of this system is revealed through the asymmetry in forward and backward transition probabilities, as is reported in this work through the simulation and theoretic analysis. In particular, our result shows prominent time irreversibility nearby the temperature interface. We propose a hidden-gyration scenario that demonstrates the source of irreversibility, while the collapse of gyrations on the one-dimensional coordinate accounts for the absence of probability current.

9 pages, 4 figures