Fluctuation-dissipation theorem in nonequilibrium steady states

In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to energy. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to entropy. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving total entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The a priori surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.

[1]  G. Diezemann.  Fluctuation-dissipation relations for Markov processes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[3]  K. Sekimoto.  Kinetic Characterization of Heat Bath and the Energetics of Thermal Ratchet Models , 1997 .

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

[5]  Udo Seifert,et al.  Stochastic thermodynamics: principles and perspectives , 2007, 0710.1187.

[6]  C. Jarzynski,et al.  Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies , 2005, Nature.

[7]  T Speck,et al.  Einstein relation generalized to nonequilibrium. , 2007, Physical review letters.

[8]  F. Ritort,et al.  The nonequilibrium thermodynamics of small systems , 2005 .

[9]  T. Hatano,et al.  Steady-state thermodynamics of Langevin systems. , 2000, Physical review letters.

[10]  M. Fuchs,et al.  Fluctuation dissipation relations in stationary states of interacting Brownian particles under shear. , 2009, Physical review letters.

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

[12]  Juan Ruben Gomez-Solano,et al.  Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a nonequilibrium steady state. , 2009, Physical review letters.

[13]  T. Speck,et al.  Extended fluctuation-dissipation theorem for soft matter in stationary flow. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  G. S. Agarwal,et al.  Fluctuation-dissipation theorems for systems in non-thermal equilibrium and applications , 1972 .

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

[16]  Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential. , 2005, Physical review letters.

[17]  I. Tinoco,et al.  Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality , 2002, Science.

[18]  M. Toda,et al.  In: Statistical physics II , 1985 .

[19]  Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state , 2005, cond-mat/0511696.

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

[21]  Takahiro Harada,et al.  Equality connecting energy dissipation with a violation of the fluctuation-response relation. , 2005, Physical review letters.

[22]  Gregory Falkovich,et al.  Fluctuation relations in simple examples of non-equilibrium steady states , 2008, 0806.1875.

[23]  Christian Maes,et al.  Fluctuations and response of nonequilibrium states. , 2009, Physical review letters.

[24]  T Speck,et al.  Measurement of stochastic entropy production. , 2006, Physical review letters.

[25]  G. Crooks.  Path-ensemble averages in systems driven far from equilibrium , 1999, cond-mat/9908420.

[26]  J. Parrondo,et al.  Generalized fluctuation-dissipation theorem for steady-state systems. , 2009, Physical review letters.

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

[28]  P Gaspard,et al.  Entropy production and time asymmetry in nonequilibrium fluctuations. , 2007, Physical review letters.

[29]  Thomas Speck,et al.  Role of external flow and frame invariance in stochastic thermodynamics. , 2007, Physical review letters.

[30]  Debra J Searles,et al.  Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. , 2002, Physical review letters.

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