Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 159, Issue 6, Pages 1286-1299Publisher
SPRINGER
DOI: 10.1007/s10955-015-1239-4
Keywords
Irreversible processes; Thermodynamic stability; Excess entropy production; Nonequilibrium free energy; Clausius heat theorem
Categories
Funding
- Belgian Interuniversity Attraction Pole [P07/18]
- Grant Agency of the Czech Republic [P204/12/0897]
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Glansdorff and Prigogine (1970) proposed a decomposition of the entropy production rate, which today is mostly known for Markov processes as the Hatano-Sasa approach. Their context was irreversible thermodynamics which, while ignoring fluctuations, still allows a somewhat broader treatment than the one based on the Master or Fokker-Planck equation. Glansdorff and Prigogine were the first to introduce a notion of excess entropy production rate EP and they suggested as sufficient stability criterion for a nonequilibrium macroscopic condition that EP be positive. We find for nonlinear diffusions that their excess entropy production rate is itself the time-derivative of a local free energy which is the close-to-equilibrium functional governing macroscopic fluctuations. The positivity of the excess EP, for which we state a simple sufficient condition, is therefore equivalent with the monotonicity in time of that functional in the relaxation to steady nonequilibrium. There also appears a relation with recent extensions of the Clausius heat theorem close-to-equilibrium. The positivity of EP immediately implies a Clausius (in)equality for the excess heat. A final and related question concerns the operational meaning of fluctuation functionals, nonequilibrium free energies, and how they make their entr,e in irreversible thermodynamics.
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