Volume 117, Number 5, March 2017
|Number of page(s)||7|
|Published online||03 May 2017|
Free energy for non-equilibrium quasi-stationary states
Yerevan Physics Institute - Alikhanian Brothers Street 2, Yerevan 375036, Armenia
Received: 10 November 2016
Accepted: 7 April 2017
We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy. Three conditions are needed for the existence of free energy in this non-equilibrium system: time-scale separation between variables of the system, partial controllability (external fields couple only with the slow variable), and an effective detailed balance. These conditions are facilitated in the continuous limit for the slow variable. In contrast to its equilibrium counterpart, the non-equilibrium free energy can increase with temperature. One example of this is that entropy reduction by means of external fields (cooling) can be easier (in the sense of the work cost) if it starts from a higher temperature.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 05.20.-y – Classical statistical mechanics
© EPLA, 2017
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