Fluctuation Theorem for Currents and Schnakenberg Network Theory

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution.

[1]  J. Rogers Chaos , 1876, Molecular Vibrations.

[2]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[3]  H. L. Dryden,et al.  Investigations on the Theory of the Brownian Movement , 1957 .

[4]  L. Onsager Reciprocal Relations in Irreversible Processes. II. , 1931 .

[5]  E. Helfand,et al.  Transport Coefficients from Dissipation in a Canonical Ensemble , 1960 .

[6]  T. L. Hill Studies in irreversible thermodynamics. IV. Diagrammatic representation of steady state fluxes for unimolecular systems. , 1966, Journal of theoretical biology.

[7]  T. L. Hill,et al.  Studies in irreversible thermodynamics. 3. Models for steady state and active transport across membranes. , 1966, Journal of theoretical biology.

[8]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[9]  T. L. Hill Thermodynamics for Chemists and Biologists , 1968 .

[10]  I. Prigogine,et al.  Fluctuations in nonequilibrium systems. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[11]  C. Desoer,et al.  Tellegen's theorem and thermodynamic inequalities. , 1971, Journal of theoretical biology.

[12]  G. Nicolis Fluctuations around nonequilibrium states in open nonlinear systems , 1972 .

[13]  G. Nicolis,et al.  A master equation description of local fluctuations , 1975 .

[14]  J. Schnakenberg Network theory of microscopic and macroscopic behavior of master equation systems , 1976 .

[15]  G. Nicolis,et al.  Stochastic analysis of a nonequilibrium phase transition: Some exact results , 1977 .

[16]  Grégoire Nicolis,et al.  Self-Organization in nonequilibrium systems , 1977 .

[17]  H. Spohn Kinetic equations from Hamiltonian dynamics: Markovian limits , 1980 .

[18]  C. Broeck,et al.  Stability criteria and fluctuations around nonequilibrium states , 1984 .

[19]  S. Swain Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .

[20]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[21]  G. Nicolis,et al.  Transport properties, Lyapunov exponents, and entropy per unit time. , 1990, Physical review letters.

[22]  Wilkins,et al.  Analytic solution for the current-voltage characteristic of two mesoscopic tunnel junctions coupled in series. , 1991, Physical review. B, Condensed matter.

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

[24]  Evans,et al.  Equilibrium microstates which generate second law violating steady states. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Dorfman,et al.  Chaotic scattering theory of transport and reaction-rate coefficients. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[27]  P. Gaspard,et al.  Fick's law and fractality of nonequilibrium stationary states in a reversible multibaker map , 1995 .

[28]  P. Gaspard,et al.  Chaotic scattering theory, thermodynamic formalism, and transport coefficients. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  G. Gallavotti,et al.  Extension of Onsager's Reciprocity to Large Fields and the Chaotic Hypothesis. , 1996, Physical review letters.

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

[31]  Jorge Kurchan,et al.  Fluctuation theorem for stochastic dynamics , 1998 .

[32]  Pierre Gaspard,et al.  Chaos, Scattering and Statistical Mechanics , 1998 .

[33]  J. Lebowitz,et al.  A Gallavotti–Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics , 1998, cond-mat/9811220.

[34]  The Fluctuation Theorem as a Gibbs Property , 1998, math-ph/9812015.

[35]  D. Ruelle Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics , 1998, chao-dyn/9812032.

[36]  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.

[37]  H. Kreuzer,et al.  Theoretical Approaches to the Kinetics off Adsorption, Desorption, and Reactions at Surfaces , 2000 .

[38]  Fractality of the hydrodynamic modes of diffusion. , 2000, nlin/0010017.

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

[40]  P. Gaspard Fluctuation theorem for nonequilibrium reactions. , 2004, The Journal of chemical physics.

[41]  D. Andrieux,et al.  Fluctuation theorem and Onsager reciprocity relations. , 2004, The Journal of chemical physics.

[42]  Christopher Jarzynski,et al.  Nonequilibrium work theorem for a system strongly coupled to a thermal environment , 2004 .

[43]  Minping Qian,et al.  Mathematical Theory of Nonequilibrium Steady States , 2004 .

[44]  Udo Seifert Entropy production along a stochastic trajectory and an integral fluctuation theorem. , 2005, Physical review letters.

[45]  D. Andrieux,et al.  Fluctuation theorem for transport in mesoscopic systems , 2006 .