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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1007/s11892-005-0054-8

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1572-9613

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Revisiting the Glansdorff–Prigogine Criterion for

Authors: Christian Maes Karel Netočný
Publish Date: 2015/03/21
Volume: 159, Issue: 6, Pages: 1286-1299
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Abstract

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 delta 2EP and they suggested as sufficient stability criterion for a nonequilibrium macroscopic condition that delta 2EP be positive We find for nonlinear diffusions that their excess entropy production rate is itself the timederivative of a local free energy which is the closetoequilibrium functional governing macroscopic fluctuations The positivity of the excess delta 2EP 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 closetoequilibrium The positivity of delta 2EP immediately implies a Clausius inequality for the excess heat A final and related question concerns the operational meaning of fluctuation functionals nonequilibrium free energies and how they make their entrée in irreversible thermodynamicsCM thanks the organizers of the Solvay Workshop P Gaspard and C Van den Broeck for giving the opportunity to present this work It was a special pleasure to do that in Brussels and with the support of the Solvay Institute where much of irreversible thermodynamics was first systematically formulated in the 1940–1970 including the contributions of Glansdorff and Prigogine that we have revisited in the light of more recent developments This work was financially supported by the Belgian Interuniversity Attraction Pole P07/18 Dygest KN gratefully acknowledges the support from the Grant Agency of the Czech Republic Grant No P204/12/0897 We are grateful to ShinIchi Sasa for encouraging discussions

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