Generalization of the second law for a transition between nonequilibrium states

Abstract The maximum work formulation of the second law of thermodynamics is generalized for a transition between nonequilibrium states. The relative entropy, the Kullback–Leibler divergence between the nonequilibrium states and the canonical distribution, determines the maximum ability to work. The difference between the final and the initial relative entropies with an effective temperature gives the maximum dissipative work for both adiabatic and isothermal processes. Our formulation reduces to both the Vaikuntanathan–Jarzynski relation and the nonequilibrium Clausius relation in certain situations. By applying our formulation to a heat engine the Carnot cycle is generalized to a circulation among nonequilibrium states.

[1]  H. Hasegawa,et al.  Generalization of the Second Law for a Nonequilibrium Initial State , 2009, 0907.1569.

[2]  T. Nieuwenhuizen,et al.  Minimal work principle: proof and counter-examples. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  J. Parrondo,et al.  Dissipation: the phase-space perspective. , 2007, Physical review letters.

[4]  Masahito Ueda,et al.  Second law of thermodynamics with discrete quantum feedback control. , 2007, Physical review letters.

[5]  G. Crooks.  Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Cohen,et al.  Dynamical Ensembles in Nonequilibrium Statistical Mechanics. , 1994, Physical review letters.

[7]  Atom cooling by nonadiabatic expansion , 2009, 0908.1483.

[8]  C. Maes,et al.  Time-Reversal and Entropy , 2002, cond-mat/0202501.

[9]  S. Sasa,et al.  Steady-state thermodynamics for heat conduction: microscopic derivation. , 2007, Physical review letters.

[10]  Masahito Ueda,et al.  Minimal energy cost for thermodynamic information processing: measurement and information erasure. , 2008, Physical review letters.

[11]  B. Gaveau,et al.  Stochastic thermodynamics and sustainable efficiency in work production. , 2010, Physical review letters.

[12]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[13]  C. Maes,et al.  Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom , 2005, cond-mat/0511419.

[14]  C. Broeck,et al.  Thermodynamic efficiency at maximum power. , 2005 .

[15]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[16]  F. Curzon,et al.  Efficiency of a Carnot engine at maximum power output , 1975 .

[17]  Suriyanarayanan Vaikuntanathan,et al.  Dissipation and lag in irreversible processes , 2009, 0909.3457.

[18]  Evans,et al.  Probability of second law violations in shearing steady states. , 1993, Physical review letters.

[19]  A. Polkovnikov.  Microscopic expression for heat in the adiabatic basis. , 2008, Physical review letters.

[20]  A. L. Kuzemsky,et al.  Nonequilibrium Statistical Thermodynamics , 2017 .

[21]  C. Jarzynski.  Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach , 1997, cond-mat/9707325.