1211.3805 (Yohei Nakayama et al.)

Second Law of Nonequilibrium Thermodynamics at Different Levels of
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Yohei Nakayama, Kyogo Kawaguchi

In the case where the dynamics of a system may be described by two or more stochastic processes at different scales, the total entropy production, the sum of Shannon entropy increment in the system and entropy production due to heat transfer, may depend on the levels of description. By analyzing general Markov stochastic processes with a parameter representing the extent of separation of time scales, we find that the excess entropy production, a key quantity in steady state thermodynamics, is invariant with respect to the change in the level of description. We demonstrate our findings in a two-dimensional overdamped Langevin model where the total entropy production differs between the levels. These results suggest that the second law-like relations involving the excess entropy production are level-independent relations even in the nonequilibrium setup, and therefore act as promising alternatives to the ordinary second law.

View original: http://arxiv.org/abs/1211.3805