## Nonequilibrium Statistcal Mechanics and Thermodynamics

*01 Feb 2019 12:06*

In equilibrium, we can use functions of states --- free energies, thermodynamic potentials --- to determine the most probable state. In fact, we can even determine the probability of arbitrary states. Out of equilibrium, it would seem that the natural generalization would be to use a functional of a sequence of states, of a trajectory, to determine the probability of trajectories. In the case of small, linear deviations from equilibrium, the Onsager-Machlup (or Onsager-Rayleigh) "action" gives us such a functional of trajectories. What works far from equilibrium? In equilibrium, one can link the thermodynamic potentials to functions which specify the rate of decay of large deviations, and this is still true out of equilibrium (see, e.g., Touchette's great review paper), but this is more of a mathematical result than a "physical" one.

Here's an argument for the ubiquity of effective actions. Markov processes
have Gibbs distributions over sequences of states, and Gibbs distributions,
just by definition, arise from an effective action. Many nonequilibrium
systems can be described by Markov processes (say, deterministic trajectory
plus noise). But I'd go further and argue that *every* nonequilbrium
system can be represented as a Markov process --- that if you haven't found
one, you're not looking hard enough. (That argument's in
a separate paper.) So it
should *always* be possible to find an effective action. But this
doesn't establish that there should be a common form for these actions across
different systems, which is what e.g., Keizer and Woo (separately) claim.

Are there universal criteria for the stability of non-equilibrium steady states, or must be actually investigate entire paths? Landauer argued for the latter, convincingly to my mind, but I need to learn more here.

Approach to equilibrium doesn't interest me so much as sustained non-equilibrium situations, but like everybody else I suppose they're strongly connected. Fluctuation-dissipation results are accordingly interesting, especially ones which do not assume nearness to equilibrium. The Evans-Searles fluctuation theorem, which is well-supported by experiments (see e.g. the Carberry et al. paper) is extremely interesting.

I should try to explain some ideas about the role of smooth dynamical systems in the statistical mechanics here, but anyone who's geeky enough to be interested really ought to read Ruelle's review article rather than listen to me, and, after that, Dorfman's book.

See also Pattern Formation; Self-organization; Self-organized Critcality; Statistical Mechanics; Foundatons of Statisticcal Mechanics; Ilya Prigogine; Stochastic Processes; Interacting Particle Systems; Large Deviations; Fluctuation-Response Relations

- Recommended:
- D. M. Carberry, J. C. Reid, G. M. Wang, E. M. Sevick, Debra
J. Searles and Denis J. Evans, "Fluctuations and Irreversibility: An
Experimental Demonstration of a Second-Law-Like Theorem Using a Colloidal
Particle Held in an Optical Trap", Physical Review Letters
**92**(2004): 140601 [An*extremely*good paper, giving a very nice explanation of the fluctuation theorem of Evans and Searles, followed by the neatest imaginable experimental demonstration of its validity.] - S. C. Chapman, G. Rowlands and Nick W. Watkins, "The Origin of Universal Fluctuations in Correlated Systems: Explicit Calculation for an Intermittent Turbulent Cascade," cond-mat/0302624
- S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics
- W. De Roeck, Christian Maes and Karel Netocny, "H-Theorems from
Autonomous Equations", Journal of
Statistical Physics
**123**(2006): 571--584, cond-mat/0508089 ["If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a Markov property for the macroscopic evolution."] - J. R. Dorfman, Introduction to Chaos in Nonequilibrium Statistical Mechanics
- S. F. Edwards, "New Kinds of Entropy", Journal of
Statistical Physics
**116**(2004): 29--42 [I need to think about how his last kind of entropy is related to Lloyd-Pagels thermodynamic depth.] - Gregory L. Eyink, "Action principle in nonequilbrium statistical
dynamics," Physical Review E
**54**(1996): 3419--3435 - K. H. Fischer and J. A. Hertz, Spin Glasses
- Dieter Forster, Hydrodynamic Fluctuations, Broken Symmetry,
and Correlation Functions [An excellent book which looks
*horrible.*Bless Donald Knuth for delivering us from type-writen equations!] - Pierre Gaspard, Chaos, Scattering and Statistical Mechanics
- A. Greven, G. Keller and G. Warnecke (eds.), Entropy
- Josef Honerkamp, Stochastic Dynamical Systems
- Giovanni Jona-Lasinio, "From fluctuations in hydrodynamics to nonequilibrium thermodynamics", arxiv:1003.4164
- Mark Kac, Probability in Physical Sciences and Related Topics
- Joel Keizer, Statistical Thermodynamics of Nonequilibrium Processes [Review: Molecular Fluctuations for Fun and Profit]
- Rolf Landauer, "Motion Out of Noisy
States," Journal of
Statistical Physics
**53**(1988): 233--248 ["The relative occupation of competing states of local stability is not determined solely by the characteristics of the locally favored states, but depends on the noise along the whole path connecting the competing states. This is not new, but the sophistication of most modern treatments has obscured the simplicity of this central point, and here it is argued for in simple physical terms."] - Michael Mackey, Time's Arrow: The Origin of Thermodynamic
Behavior [This is a very valuable short introduction to the
ergodic theory of Markov operators, which is
highly relevant to the origins of irreversibility, etc., but I don't think his
approach works, because he focuses on the
*relative*entropy (Kullback-Leibler divergence from the invariant distribution), rather than the Boltzmann entropy or even the Gibbs entropy.] - Mark Millonas (ed.), Fluctuations and Order: The New Synthesis [Despite the subtitle, no synthesis is in evidence. However, many of the individual papers are very interesting.]
- Lars Onsager, "Reciprocal relations in irreversible processes",
Physical Review
**37**(1931): 405--426 (part I) and**38**(1931): 2265--2279 (part II) - Lars Onsager and S. Machlup, "Fluctuations and Irreversible
Processes", Physical Review
**91**(1953): 1505--1512 - David Ruelle, "Smooth Dynamics and New Theoretical Ideas in
Nonequilibrium Statistical Mechanics," Journal of Statistical
Physics
**95**(1999): 393--468 = chao-dyn/9812032 - Geoffrey Sewell, Quantum Mechanics and Its Emergent Macrophysics [Including nonequilibrium quantum statistical mechanics]
- Eric Smith
- "Thermodynamic dual structure of linear-dissipative
driven systems", Physical
Review E
- "Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions", arxiv:1102.3938

**72**(2005): 036130 - Hyung-June Woo, "Statistics of nonequilibrium trajectories and
pattern
selection", Europhysics
Letters
**64**(2003): 627--633 - R. K. P. Zia, L. B. Shaw, B. Schmittmann and R. J. Astalos, "Contrasts Between Equilibrium and Non-Equilibrium Steady States: Computer Aided Discoveries in Simple Lattice Gases," cond-mat/9906376

- Modesty forbids me to recommend:
- CRS and Cristopher Moore, "What Is a Macrostate? Subjective Measurements and Objective Dynamics," cond-mat/03003625

- To read:
- D. Abreu, U. Seifert, "Thermodynamics of genuine non-equilibrium states under feedback control", arxiv:1109.5892
- Tameem Albash, Daniel A. Lidar, Milad Marvian, and Paolo Zanardi, "Fluctuation theorems for quantum processes", Physical Review E
**88**(2013): 032146 - D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, and
A. Petrosyan, "Entropy Production and Time Asymmetry in Nonequilibrium
Fluctuations", Physical Review
Letters
**98**(2007): 150601 - Francis J. Alexander and Gregory L. Eyink, "Rayleigh-Ritz
Calculation of Effective Potential Far from Equilibrium," Physical Review
Letters
**78**(1997): 1--4 - Bidhan Chandra Bag
- "Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production," cond-mat/0205500
- "Upper bound for the time derivative of entropy for nonequilibrium stochastic processes," cond-mat/0201434
- BCB, Suman Kumar Banik, and Deb Shankar Ray, "The noise properties of stochastic processes and entropy production," cond-mat/0104524

- M. M. Bandi, J. R. Cressman Jr., W. I. Goldburg, "Test of the Fluctuation Relation in compressible turbulence on a free surface", nlin.CD/0607037
- M. M. Bandi, W. I. Goldburg, J. R. Cressman Jr, "Measurement of entropy production rate in compressible turbulence", nlin.CD/0607036
- Julien Barre', Freddy Bouchet, Thierry Dauxois, Stefano Ruffo, "Out-of-equilibrium states as statistical equilibria of an effective dynamics," cond-mat/0204407
- Daniel A. Beard and Hong Qian, "Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Chemical Reactions", q-bio.SC/0607020
- Christian Beck
- "Superstatistics in hydrodynamic turbulence," physics/0303061
- "Superstatistics: Theory and Applications," cond-mat/0303288

- Eric Bertin, Kirsten Martens, Olivier Dauchot, and Michel Droz,
"Intensive thermodynamic parameters in nonequilibrium systems",
Physical Review
E
**75**(2007): 031120 - Eric Bertin, Olivier Dauchot, Michel Droz, "Definition and
relevance of nonequilibrium intensive thermodynamic
parameters", Physical
Review Letters
**96**(2006): 120601, cond-mat/0512116 - L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim
- "Current Fluctations in Stochastic Lattice Gases",
Physical Review
Letters
**94**(2005): 030601 = cond-mat/0407161 - "Towards a Nonequilibrium Thermodynamics: A Self-Contained Macroscopic Description of Driven Diffusive Systems", Journal of Statistical Physics
**135**(2009): 857--872 - "Lagrangian phase transitions in nonequilibrium thermodynamic systems", arxiv:1005.1489
- "Large deviation approach to non equilibrium processes in stochastic lattice gases", arxiv:math/0602557

- "Current Fluctations in Stochastic Lattice Gases",
Physical Review
Letters
- Richard A. Blythe, "An introduction to phase transitions in stochastic dynamical systems", cond-mat/0511627
- Doriano Brogioli, "Marginally Stable Chemical Systems as Precursors
of
Life", Physical
Review Letters
**105**(2010): 058102 - Stephen G. Brush, The Kind of Motion We Call Heat: Statistical Physics and Irreversible Processes
- A. A. Budini and M.O. Caceres, "Functional characterization of generalized Langevin equations", cond-mat/0402311 [Abstract: "We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the noise, neither the fluctuation dissipation theorem. We found that the characteristic functional of the linear process can be expressed in terms of noise's functional and the Green function of the deterministic (memory-like) dissipative dynamics. This object allow us to get a procedure to calculate all the Kolmogorov hierarchy of the non-Markov process. As examples we have characterized through the 1-time probability a noise-induced interplay between the dissipative dynamics and the structure of different noises. Conditions that lead to non-Gaussian statistics and distributions with long tails are analyzed. The introduction of arbitrary fluctuations in fractional Langevin equations have also been pointed out."]
- Giovanni Bussi, Alessandro Laio and Michele Parrinello,
"Equilibrium Free Energies from Nonequilibrium Metadynamics",
Physical Review
Letters
**96**(2006): 090601 - C. Bustamante, J. Liphardt, and F. Ritort, "The Nonequilibrium
Thermodynamics of Small Systems", Physics
Today
**58**(2005): 43--48 = cond-mat/0511629 - Pasquale Calabrese and Andrea Gambassi, "On the definition of a unique effective temperature for non-equilibrium critical systems", cond-mat/0406289
- T. Carlsson, L. Sjogren, E. Mamontov, and K. Psiuk-Maksymowicz,
"Irreducible memory function and slow dynamics in disordered systems",
Physical Review
E
**75**(2007): 031109 - M. E. Cates and M. R. Evans (eds.), Soft and Fragile Matter: Nonequilibrium Dynamics, Metastability and Flow
- Vladimir Y. Chernyak, Mcihael Chertkov and Christopher Jarzynski, "Path-integral analysis of fluctuation theorems for general Langevin processes", cond-mat/0605471
- Philippe Chomaz, Francesca Gulminelli and Olivier Juillet, "Generalized Gibbs ensembles for time dependent processes", cond-mat/0412475
- E. G. D. Cohen, "Properties of nonequilibrium steady states: a path integral approach", Journal of Statistical Mechanics (2008): P07014
- Leonardo Crochik and Tania Tome, "Entropy production in the
majority-vote model", Physical
Review E
**72**(2005): 057103 - Daan Crommelin, "Estimation of Space-Dependent Diffusions and Potential Landscapes from Non-equilibrium Data", Journal of Statistical Physics
**149**(2012): 220--233 - Gavin E. Crooks, "Measuring Thermodynamic Length",
Physical Review
Letters
**99**(2007): 100602, arxiv:0706.0559 ["Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao's entropy differential metric."] - Gregory Bulnes Cuetara, Massimiliano Esposito, Alberto Imparato, "Exact fluctuation theorem without ensemble quantities", arxiv:1402.1873
- B. Derrida, "Non equilibrium steady states: fluctuations and large deviations of the density and of the current", cond-mat/0703762
- B. Derrida, Joel L. Lebowitz and Eugene R. Speer, "Exact Large Deviation Functional for the Density Profile in a Stationary Nonequilibrium Open System," cond-mat/0105110
- Deepak Dhar, "Pico-canonical ensembles: A theoretical description of metastable states," cond-mat/0205011
- Ronald Dickman and Ronaldo Vidigal, "Path Integrals and Perturbation Theory for Stochastic Processes", cond-mat/0205321
- Jean-Pierre Eckmann, "Non-equilibrium steady states", math-ph/0304043
- Andreas Eibeck and Wolfgang Wagner, "Stochastic Interacting
Particle Systems and Nonlinear Kinetic
Equations", Annals of
Applied Probability
**13**(2003): 845--889 - Vlad Elgart and Alex Kamenev, "Rare Events Statistics in Reaction--Diffusion Systems", cond-mat/0404241 [i.e., large deviations]
- Denis J. Evans and Gary Morriss, Statistical Mechanics of Nonequilibrium Liquids
- R. M. L. Evans
- "Detailed balance has a counterpart in non-equilibrium steady states", cond-mat/0408614
- "Rules for transition rates in nonequilibrium steady states", cond-mat/0402527

- Massimo Falcioni, Luigi Palatella, Simone Pigolotti, Lamberto Rondoni and Angelo Vulpiani, "Boltzmann entropy and chaos in a large assembly of weakly interacting systems", nlin.CD/0507038
- Gregory Falkovich and Alexander Fouxon, "Entropy production away from equilibrium", nlin.CD/0312033 ["we express the entropy production via a two-point correlation function... the long-time limit gives the sum of the Lyapunov exponents"]
- Roger Filliger and Max-Olivier Hongler, "Relative entropy and
efficiency measure for diffusion-mediated transport processes", Journal of Physics A:
Mathematical and General
**38**(2005): 1247--1255 ["We propose an efficiency measure for diffusion-mediated transport processes including molecular-scale engines such as Brownian motors.... Ultimately, the efficiency measure can be directly interpreted as the relative entropy between two probability distributions, namely: the distribution of the particles in the presence of the external rectifying force field and a reference distribution describing the behavior in the absence of the rectifier". Interesting for the link between relative entropy and energetics.] - Silvio Franz, "How glasses explore configuration space," cond-mat/0212091
- Henryk Fuks and Nino Boccara, "Convergence to equilibrium in a class of interacting particle systems evolving in discrete time," nlin.CG/0101037
- Giovanni Gallavotti
- "Entropy creation in nonequilibrium thermodynamics: a review", cond-mat/0312657
- "Stationary nonequilibrium statistical mechanics", cond-mat/0510027
- "Fluctuation relation, fluctuation theorem, thermostats and entropy creation in non equilibrium statistical Physics", cond-mat/0612061

- J. Galvao Ramos, Aurea R. Vasconcellos and Roberto Luzzi, "Nonlinear Higher-Order Thermo-Hydrodynamics II: Illustrative Examples", cond-mat/0412231
- Piotr Garbaczewski
- "Information Entropy Balance and Local Momentum Conservation Laws in Nonequilibrium Random Dynamics," cond-mat/0301044
- "Shannon versus Kullback-Leibler Entropies in Nonequilibrium Random Motion", cond-mat/0504115

- Nicolas B. Garnier and Daniel K. Wojcik, "Spatiotemporal Chaos: The
Microscopic Perspective", Physical Review
Letters
**96**(2006): 114101 - Pierre Gaspard, "Time-Reversed Dynamical Entropy and
Irreversibility in Markovian Random Processes", Journal of Statistical
Physics
**117**(2004): 599--615 - T. Gilbert, J. R. Dorfman and P. Gaspard, "Entropy Production,
Fractals, and Relaxation to Equilibrium," Physical Review Letters
**85**(2000): 1606--1609 - S. Goldstein and J. L. Lebowitz, "On the (Boltzmann) Entropy of Nonequilibrium Systems," cond-mat/0304251
- S. Goldsten, J. L. Lebowitz and Y. Sinai, "Remark on the (Non)convergence of Ensemble Densities in Dynamical Systems," math-ph/9804016
- Giacomo Gradenigo, Alessandro Sarracino, Andrea Puglisi, Hugo Touchette, "Fluctuation relations without uniform large deviations", Journal of Physics A
**46**(2013): 335002, arxiv:1303.2851 - T. Hanney and R. B. Stinchcombe, "Real-space renormalisation group approach to driven diffusive systems", cond-mat/0606515
- R. J. Harris, A. Rákos, G. M. Schuetz, "Breakdown of Gallavotti-Cohen symmetry for stochastic dynamics", cond-mat/0512159
- Hisao Hayakawa and Michio Otsuki, "Nonequilibrium identities and response theory for dissipative particles", Physical Review E
**88**(2013): 032117 - Kumiko Hayashi and Hiroaki Takagi, "Fluctuation Thoerem applied
to Dictyostelium discoideum system", Journal of the Physical
Society of Japan
**10**(2007): 105001, arxiv:0710.0523 - Kumiko Hayashi, Hiroshi Ueno, Ryota Iino, and Hiroyuki Noji,
"Fluctuation Theorem Applied to F1-ATPase", Physical
Review Letters
**104**(2010): 218103 - Malte Henkel, "Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance", cond-mat/0609672
- Haye Hinrichsen, "Critical Phenomena in Nonequilibrium Systems," cond-mat/0001070
- Steven Huntsman, "Effective statistical physics of Anosov systems", arxiv:1009.2127
- Pablo I. Hurtado, Carlos Pérez-Espigares, Jesús J. del Pozo, and Pedro L. Garrido, "Symmetries in fluctuations far from equilibrium",
Proceedings of the National Academy
of Sciences (USA)
**108**(2011): 7704--7709 - A. Imparato and L. Peliti
- "Work probability distribution in systems driven out of equilibrium", cond-mat/0507080
- "The distribution function of entropy flow in stochastic systems", cond-mat/0611078

- Claude Itzykson and Jean-Michel Drouffe, Statistical Field Theory (2 vols.)
- M. V. Ivanchenko, O. I. Kanakov, V. D. Shalfeev and S. Flach,
"Discrete breathers in transient processes and thermal
equilibrium", Physica D
**198**(2004): 120--135 - Dominik Janzing, "On the Entropy Production of Time Series with
Unidirectional
Linearity", Journal
of Statistical Physics
**138**(2010): 767--779 [Open access] - Christopher Jarzynski, "Comparison of far-from-equilibrium work relations", cond-mat/0612305
- Owen Jepps, Denis J. Evans and Debra J. Searles, "The fluctuation theorem and Lyapunov weights," cond-mat/0311090
- Alex Kamenev, Field Theory of Non-Equilibrium Systems
- Dragi Karevski, "Foundations of Statistical Mechanics: in and out of Equilibrium", cond-mat/0509595
- Kyogo Kawaguchi and Yohei Nakayama, "Fluctuation theorem for hidden entropy production", Physical Review E
**88**(2013): 022147 - R. Kawai, J. M. R. Parrondo, C. Van den Broeck, "Dissipation: The phase-space perspective", cond-mat/0701397
- Teruhisa S. Komatsu and Naoko Nakagawa, "Expression for the
Stationary Distribution in Nonequilibrium Steady
States", Physical Review
Letters
**100**(2008): 030601 - Teruhisa S. Komatsu, Naoko Nakagawa, Shin-Ichi Sasa and Hal Tasaki,
"Representation of Nonequilibrium Steady States in Large Mechanical
Systems", Journal
of Statistical Physics
**134**(2009): 401--423 - Pavel L. Krapivsky, Sidney Redner and Eli Ben-Naim, A Kinetic View of Statistical Physics
- Anupam Kundu, "Nonequilibrium fluctuation theorem for systems under discrete and continuous feedback control", Physical Review E
**86**(2012): 021107 - Jorge Kurchan, "Six out of equilibrium lectures", arxiv:0901.1271
- Michal Kurzynski, The Thermodynamic Machinery of Life
- Hernan Larralde, Francois Leyvraz, and David P. Sanders, "Metastability in Markov processes", cond-mat/0608439 = Journal of Statistical Mechanics (2006): P08013
- Joel L. Lebowitz, "Boltzmann's Entropy and Large Deviation Lyapunov Functionals for Closed and Open Macroscopic Systems", arxiv:1112.1667
- Raphael Lefevere, "On the local space-time structure of non-equilibrium steady states", math-ph/0609049
- Dino Leporini and Roberto Mauri, "Fluctuations of non-conservative systems", Journal of Statistical Mechanics: Theory and Experiment
**2007**: P03002 - Francois Leyvraz, Hernan Larralde, and David P. Sanders, "A Definition of Metastability for Markov Processes with Detailed Balance", cond-mat/0509754
- Katja Lindenberg and Bruce West, The Nonequilibrium Statistical Mechanics of Open and Closed Systems
- S. Lubeck, "Universal scaling behavior of non-equilibrium phase transitions", cond-mat/0501259 [160 pp. review]
- David Luposchainsky, Andre Cardoso Barato, Haye Hinrichsen, "Strong fluctuation theorem for nonstationary nonequilibrium systems", Physical Review E
**87**(2013): 042108, arxiv:1302.1013 - James F. Lutsko, "Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid", cond-mat/0510749
- Michael C. Mackey and Marta Tyran-Kaminska, "Temporal Behavior of the Conditional and Gibbs' Entropies", cond-mat/0509649 [Weirdly, what Mackey calls "conditional entropy" is what everyone else calls "relative entropy" or "Kullback-Leibler divergence", and not at all what everyone else calls "conditional entropy".]
- Christian Maes
- "Entropy Production in Driven Spatially Extended Systems," cond-mat/0101064
- "Elements of Nonequilibrium Statistical Mechanics" [PDF]
- "Statistical Mechanics of Entropy Production: Gibbsian hypothesis and local fluctuations," cond-mat/0106464

- Christian Maes and Karel Netocny
- "Time-Reversal and Entropy," cond-mat/0202501
- "Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states", arixv:0705.2344

- C. Maes, K. Netocny, B. Shergelashvili, "A selection of nonequilibrium issues", math-ph/0701047 [Lecture notes, 55 pp.]
- Christian Maes, Karel Netocny, Bram Wynants
- "On and beyond entropy production: the case of Markov jump processes", arxiv:0709.4327
- "Dynamical fluctuations for semi-Markov processes", Journal of Physics A
**42**(2009): 365002, arxiv:0905.4897 - "Monotonic Return to Steady Nonequilibrium",
Physical Review Letters
**107**(2011): 010601

- Christian Maes, Frank Redig and Michel Verschuere
- "From Global to Local Fluctuation Theorems," cond-mat/0106639
- "No current without heat," cond-mat/0111281

- Christian Maes, Hal Tasaki, "Second law of thermodynamics for macroscopic mechanics coupled to thermodynamic degrees of freedom", cond-mat/0511419
- Christian Maes and Maarten H. van Wieren, "Time-Symmetric
Fluctuations in Nonequilibrium Systems", Physical Review
Letters
**96**(2006): 240601 = cond-mat/0601299 - Ferenc Markús and Katalin Gambár, "Generalized
Hamilton-Jacobi equation for simple dissipative processes", Physical
Review E
**70**(2004): 016123 [link] - Joaquin Marro and Ronald Dickman, Nonequilibrium Phase Transitions in Lattice Models
- Daniel C. Mattis and M. Larence Glasser, "The Uses of Quantum
Field Theory in Diffusion-Limited Reactions", Reviews of Modern Physics
**70**(1998): 979--1001 - Paul Meakin, Fractals, Scaling and Growth Far from Equilibrium
- S. S. Melnyk, O. V. Usatenko, and V. A. Yampol'skii, "Memory Functions of the Additive Markov chains: Applications to Complex Dynamic Systems", physics/0412169
- Guillaume Michel and Debra J. Searles
- "Local Fluctuation Theorem for Large Systems", Physical Review Letters
**110**(2013): 260602 - "Contribution of the stochastic forces to the fluctuation theorem", Physical Review E
**85**(2012): 042102

- "Local Fluctuation Theorem for Large Systems", Physical Review Letters
- Emil Mittag and Denis J. Evans, "Time-dependent fluctuation
theorem," Physical Review E
**67**(2003): 026113 - Geza Odor, "Phase transition universality classes of classical,
nonequilibrium systems," cond-mat/0205644 = Reviews of Modern Physics
**76**(2004): 663--724 [145pp. review] - Hans Christian Ottinger, "Weakly and Strongly Consistent
Formulations of Irreversible
Processes", Physical Review
Letters
**99**(2007): 130602 - Agusti Perez-Madrid, "Molecular Theory of Irreversibility", cond-mat/0509491
- Hans L. Pécseli, Fluctuations in Physical Systems
- Mark Pollicott and Richard Sharp, "Large Deviations, Fluctuations and Shrinking Intervals", Communications
in Mathematical Physics
**290**(2009): 321--334 - Noëlle Pottier, Nonequilibrium Statistical Physics: Linear Irreversible Processes [Favorable review in J. Stat. Phys.]
- Hong Qian
- "A Gallavotti-Cohen-Type Symmetry in the Steady-state Kinetics of Single Enzyme Turnover Reactions", cond-mat/0507659
- "Relative Entropy: Free Energy Associated with Equilibrium
Fluctuations and Nonequilibrium
Deviations", math-ph/0007010
= Physical
Review E
**63**(2001): 042103

- Hong Qian and Timothy C. Reluga, "Nonequilibrium Thermodynamics and
Nonlinear Kinetics in a Cellular Signaling Switch", Physical Review
Letters
**94**(2005): 028101 - Saar Rahav and Christopher Jarzynski, "Fluctuation relations and coarse-graining", arxiv:0708.2437 = Journal of Statistical Mechanics (2007): P09012
- Jorgen Rammer, Quantum Field Theory of Non-equilibrium States
- J. C. Reid, D. M. Carberry, G. M. Wang, E. M. Sevick, Denis
J. Evans and Debra J. Searles, "Reversibility in nonequilibrium trajectories of
an optically trapped particle", Physical Review
E
**70**(2004): 016111 [link] - Pedro M. Reis, Rohit A. Ingale, Mark D. Shattuck, "Universal velocity distributions in an experimental granular fluid", cond-mat/0611024 [Measurable departures from the Maxwell-Boltzmann distribution, in accordance with theory...]
- F. Ritort, "Single molecule experiments in biophysics: exploring the thermal behavior of nonequilibrium small systems", cond-mat/0509606 [Review]
- Edgar Roldan, Juan M.R. Parrondo, "Estimating dissipation from single stationary trajectories", arxiv:1004.2831
- L. Rondoni and E. G. D. Cohen, "Gibbs Entropy and Irreversible Thermodynamics," cond-mat/9908367
- Lamberto Rondoni, Carlos Mejia-Monasterio, "Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms", arxiv:0709.1976
- David Ruelle
- "Extending the definition of entropy to nonequilibrium steady states," cond-mat/0303156
- "Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics", Proceedings of the National Academy of Sciences (USA)
**109**(2012): 20344--20346

- Stefano Ruffo, "Equilibrium and nonequilibrium properties of systems with long-range interactions", European Physical Journal B
**64**(2008): 355--363, arxiv:0711/1173 - Himadri S. Samanta and J. K. Bhattacharjee, "Non equilibrium statistical physics with fictitious time", cond-mat/0509563
- Shin-ichi Sasa
- "Physics of Large Deviation", arxiv:1204.5584
- "Derivation of Hydrodynamics from the Hamiltonian description of particle systems", Physical Review Letters
**112**(2014): 100602, arxiv:1306.4880

- Shin-ichi Sasa and Teruhisa S. Komats
- "Steady state thermodynamics", cond-mat/0411052 [82pp. tome]
- "Thermodynamic Entropy and Excess Information Loss in Dynamical Systems with Time-Dependent Hamiltonian," chao-dyn/9807010
- "Thermodynamic Irreversibility from High-Dimensionl Hamiltonian Chaos," cond-mat/9911181

- B. Schmittmann and R. K. P. Zia, Statistical Mechanics of Driven Diffusive Systems
- Debra J. Searles and Denis J. Evans
- "Fluctuation Theorem for Stochastic Systems,"
Physical Review E
**60**(1999): 159--164 = cond-mat/9901258 - "The Fluctuation Theorem and Green-Kubo Relations," cond-mat/9902021
- "Ensemble Dependence of the Transient Fluctuation Theorem," cond-mat/9906002

- "Fluctuation Theorem for Stochastic Systems,"
Physical Review E
- Udo Seifert
- "Entropy production along a stochastic trajectory and
an integral fluctuation theorem", cond-mat/0503686 = Physical Review
Letters
**95**(2005): 040602 - "Stochastic thermodynamics: principles
and perspectives", European Physical Journal B
**64**(2008): 423--431, arxiv:0710.1187

- "Entropy production along a stochastic trajectory and
an integral fluctuation theorem", cond-mat/0503686 = Physical Review
Letters
- E.M. Sevick, R. Prabhakar, Stephen R. Williams, Debra J. Searles, "Fluctuation Theorems", arxiv:0709.3888
- Geoffrey Sewell [Note to self: carefully compare these to papers by
Woo]
- "On Connections between the Quantum and Hydrodynamical Pictures of Matter", arxiv:0710.1239
- "Quantum macrostatistical picture of nonequilibrium steady states", math-ph/0403017
- "Quantum Macrostatistical Theory of Nonequilibrium Steady States", math-ph/0509069
- "Quantum Theory of Irreversibility: Open Systems and Continuum Mechanics", pp. 7--30 in E. Benatti and R. Floreanini (eds.): Lecture Notes in Physics vol. 622 (Springer-Verlag, 2003)
- "Macrostatistics and Fluctuating Hydrodynamics", arxiv:1206.2750

- T. Speck and U. Seifert, "The Jarzynski relation, fluctuation theorems, and stochastic thermodynamics for non-Markovian processes", Journal of Statistical Mechanics (2007) L09002, arxiv:0709.2236
- Jaeyoung Sung, "Validity condition of the Jarzynski relation for a classical mechanical system", cond-mat/0506214
- Tooru Taniguchi, E. G. D. Cohen, "Onsager-Machlup theory for
nonequilibrium steady states and fluctuation
theorems", cond-mat/0605548
=? Journal
of Statistical Physics
**130**(2007): 633--667 - Hal Tasaki
- "From Quantum Dynamics to the Second Law of Thermodynamics," cond-mat/0005128
- "The second law of Thermodynamics as a theorem in quantum mechanics," cond-mat/0011321

- Uwe C. Tauber, "Field Theory Approaches to Nonequilibrium Dynamics", cond-mat/0511743
- C. Tietz, S. Schuler, T. Speck, U. Seifert, and J. Wrachtrup,
"Measurement of Stochastic Entropy Production", Physical Review
Letters
**97**(2006): 050602 = cond-mat/0607407 - Alexei V. Tkachenko, "Generalized Entropy Approach to Far-from-Equilibrium Statistical Mechanics," cond-mat/0005198
- H. Touchette and E. G. D. Cohen, "A novel fluctuation relation for
a Lévy
particle", cond-mat/0703254
=? Physical Review
E
**76**(2007) 020101 - H. Touchette, M. Costeniuc, R.S. Ellis, and B. Turkington, "Metastability within the generalized canonical ensemble", cond-mat/0509802
- Hugo Touchette, Rosemary J. Harris, "Large deviation approach to nonequilibrium systems", arxiv:1110.5216
- E. H. Trepagnier, C. Jarzynski, F. Ritort, G. E. Crooks, C. J.
Bustamante and J. Liphardt, "Experimental test of Hatano and Sasa's
nonequilibrium steady-state equality", Proceedings of the
National Academy of Sciences USA
**101**(2004): 15033--15037 - Bruce Turkington, "An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics", Journal of Statistical Physics
**152**(2013): 569--597, arxiv:1207.2692 - Ramses van Zon, H. van Beijeren and J. R. Dorfman, "Kinetic Theory of Dynamical Systems," chao-dyn/9906040
- Aurea R. Vasconcellos, J. Galvao Ramos and Roberto Luzzi, "Nonlinear Higher-Order Thermo-Hydrodynamics: Generalized Approach in a Nonequilibrium Ensemble Formalism", cond-mat/0412227
- G. M. Wang, J. C. Reid, D. M. Carberry, D. R. M. Williams,
E. M. Sevick, and Denis J. Evans, "Experimental study of the fluctuation
theorem in a nonequilibrium steady state", PRE
**71**(2005): 046142 - Stephen R. Williams, Debra J. Searles, Denis J. Evans, "Numerical study of the Steady State Fluctuation Relations Far from Equilibrium", cond-mat/0601328
- Hyung-June Woo, "Variational
formulation of nonequilibrium thermodynamics for hydrodynamic pattern
formations," Physical Review E
**66**(2002) 066104 - Jeroen Wouters, Valerio Lucarini, "Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach",
Journal of Statistical Physics
**151**(2013): 850--860, arxiv:1208.3080 - Bram Wynants, "Structures of nonequilibrium fluctuations: dissipation and activity", arxiv:1011.4210
- V. I. Yukalov, "Principle of Pattern Selection for Nonequilibrium Phenomena," cond-mat/0110107
- Francesco Zamponi, "Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence", cond-mat/0612019
- Juan Zanella and Esteban Calzetta, "Renormalization group and
nonequilibrium action in stochastic field theory,"
Physical Review
E
**66**(2002): 036134 - H. D. Zeh, Physical Basis of the Direction of Time
- R. K. P. Zia, B. Schmittmann, "A possible classification of nonequilibrium steady states", cond-mat/0605301
- D. N. Zubarev et al., Statistical Mechanics of Nonequilibrium Processes
- Robert Zwanzig, Nonequilibrium Statistical Mechanics

- To write someday, when I'd understand it:
- "Variational Principles in Nonequilibrium Statistical Mechanics"