Reversal symmetries for cyclic paths in systems far from thermodynamic equilibrium
Dr. John W. Biddle
Holy Cross College
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 between states will occur with the same frequency in the forward as in the reverse direction. However, if expenditure of energy maintaining the system away from equilibrium changes the rate of even a single transition, such time-reversal symmetry undergoes a widespread breakdown reaching far beyond the point at which the energy is expended. System properties that are locally determined at equilibrium then come to depend in a complicated manner on the rate of every transition in the system. Cyclic paths, however, have reversibility properties that remain locally determined, and which can exhibit reversal 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 long-time limit, only by the thermodynamic force on the cycle itself. In particular, if there is no net energy expenditure on the cycle, then the cycle occurrence frequencies are the same in either direction in the long-time limit.
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