Reversal symmetries for cyclic paths away from thermodynamic equilibrium
Abstract
If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if expenditure of energy changes the rate of even a single transition to yield a nonequilibrium steady state, such timereversal symmetry undergoes a widespread breakdown, far beyond the point at which the energy is expended. An explosion of interdependency also arises, with steadystate probabilities of system states depending in a complicated manner on the rate of every transition in the system. Nevertheless, in the midst of this global nonequilibrium complexity, we find that cyclic paths have reversibility properties that remain local, and which can exhibit symmetry, no matter how far the system is from thermodynamic equilibrium. Specifically, given any cycle of reversible transitions, the ratio of the frequencies with which the cycle occurs in one direction versus the other is determined, in the longtime limit, only by the thermodynamic force on the cycle itself, without requiring knowledge of transition rates elsewhere in the system. In particular, if there is no net energy expenditure on the cycle, then, over long times, the cycle occurrence frequencies are the same in either direction.
 Publication:

Physical Review E
 Pub Date:
 June 2020
 DOI:
 10.1103/PhysRevE.101.062125
 arXiv:
 arXiv:1910.03735
 Bibcode:
 2020PhRvE.101f2125B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Biological Physics
 EPrint:
 10 pages, 3 figures. Central results unchanged from previous version. Added figures and text to better illustrate results in context of particular system. Added references and added to Discussion to situate results in context of related research. Fixed typographical errors, error in figure legend