In equilibrium, we can use functions of states --- free energies,thermodynamic potentials --- to determine the most probable state. In fact, wecan even determine the probability of arbitrary states. Out of equilibrium, itwould seem that the natural generalization would be to use a functional of asequence of states, of a trajectory, to determine the probability oftrajectories. In the case of small, linear deviations from equilibrium, theOnsager-Machlup (or Onsager-Rayleigh) "action" gives us such a functional oftrajectories. What works far from equilibrium? In equilibrium, one can linkthe thermodynamic potentials to functions which specify the rate of decayof large deviations, and this is still trueout of equilibrium (see, e.g., Touchette's great review paper), but this ismore of a mathematical result than a "physical" one.Here's an argument for the ubiquity of effective actions. Markov processeshave Gibbs distributions over sequences of states, and Gibbs distributions,just by definition, arise from an effective action. (*) Many nonequilibriumsystems can be described by Markov processes (say, deterministic trajectoryplus noise). But I'd go further and argue that every nonequilbriumsystem can be represented as a Markov process --- that if you haven't foundone, you're not looking hard enough. (That argument's ina separate paper.) So itshould always be possible to find an effective action. But thisdoesn't establish that there should be a common form for these actions acrossdifferent systems, which is what e.g., Keizer and Woo (separately) claim.Are there universal criteria for the stability of non-equilibrium steadystates, or must be actually investigate entire paths? Landauer argued for thelatter, convincingly to my mind, but I need to learn more here.Approach to equilibrium doesn't interest me so much as sustainednon-equilibrium situations, but like everybody else I suppose they're stronglyconnected. Fluctuation-dissipation results are accordingly interesting,especially ones which do not assume nearness to equilibrium. The Evans-Searlesfluctuation 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 dynamicalsystems in the statistical mechanics here, but anyone who's geeky enough to beinterested really ought to read Ruelle's review article rather than listen tome, and, after that, Dorfman's book.*: Pedantically, a Gibbs distribution over a collection of variables \( X_t \), index by \( \mathcalT \), collectively \( X \), will take the form \( \mathbbP(X=x) \propto e^-u(x) \), and the "potential" \( u(x) = \sum_A \in 2^\mathcalTu_A(x_A) \), where \( u_A \) is a function only of the values of the random variables at the indices \( A \). (Obvious measure-theoretic complications for continuous index sets are obvious.) The sets \( A \) which actually contribute to the potential are called "cliques". In the particular case of Markov processes in discrete time, the cliques are pairs of successive indices \( \left\ t, t+1 \right\ \), so we can think of \( u(x) \) as being basically a discrete-time effective action. For continuous-time Markov processes, see under Path Integrals and Feynman Diagrams for Classical Stochastic Processes.See alsoFluctuation-Response Relations;Foundatons of Statistical Mechanics;Interacting Particle Systems;Large Deviations;Mori-Zwanzig Formalism;Pattern Formation;Ilya Prigogine;Self-organization;Self-organized Critcality;Statistical Mechanics;Stochastic Processes;Recommended, big picture:S. R. de Groot and P. Mazur, Non-EquilibriumThermodynamicsJ. R. Dorfman, Introduction to Chaos in NonequilibriumStatistical MechanicsDieter Forster, Hydrodynamic Fluctuations, Broken Symmetry,and Correlation Functions [An excellent book which lookshorrible. Bless Donald Knuth for delivering us from type-writenequations!]Josef Honerkamp, Stochastic Dynamical SystemsJoel Keizer, Statistical Thermodynamics of NonequilibriumProcesses [Review: Molecular Fluctuationsfor Fun and Profit]David Ruelle, "Smooth Dynamics and New Theoretical Ideas inNonequilibrium Statistical Mechanics," Journal of StatisticalPhysics 95 (1999): 393--468 = chao-dyn/9812032Geoffrey Sewell, Quantum Mechanics and Its EmergentMacrophysics [Including nonequilibrium quantum statistical mechanics]Eric Smith, "Large-deviation principles, stochastic effectiveactions, path entropies, and the structure and meaning of thermodynamicdescriptions", arxiv:1102.3938Hugo Touchette, "The Large Deviations Approach to StatisticalMechanics", Physics Reports 478 (2009): 1--69, arxiv:0804.0327Recommended, historical:Mark Kac, Probability in Physical Sciences and RelatedTopicsLars Onsager, "Reciprocal relations in irreversible processes",Physical Review37 (1931):405--426 (part I)and 38(1931): 2265--2279 (part II)Lars Onsager and S. Machlup, "Fluctuations and IrreversibleProcesses", Physical Review 91 (1953):1505--1512Recommended, close-ups:D. M. Carberry, J. C. Reid, G. M. Wang, E. M. Sevick, DebraJ. Searles and Denis J. Evans, "Fluctuations and Irreversibility: AnExperimental Demonstration of a Second-Law-Like Theorem Using a ColloidalParticle Held in an Optical Trap", Physical Review Letters92 (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 ofUniversal Fluctuations in Correlated Systems: Explicit Calculation for anIntermittent Turbulent Cascade," cond-mat/0302624W. De Roeck, Christian Maes and Karel Netocny, "H-Theorems fromAutonomous Equations", Journal ofStatistical Physics 123 (2006): 571--584, cond-mat/0508089["Iffor a Hamiltonian dynamics for many particles, at all times the presentmacrostate determines the future macrostate, then its entropy is non-decreasingas a consequence of Liouville's theorem. That observation, made since long, ishere rigorously analyzed with special care to reconcile the application ofLiouville's theorem (for a finite number of particles) with the condition ofautonomous macroscopic evolution (sharp only in the limit of infinite scaleseparation); and to evaluate the presumed necessity of a Markov property forthe macroscopic evolution."]S. F. Edwards, "New Kinds of Entropy", Journal ofStatistical Physics 116 (2004): 29--42 [I need tothink about how his last kind of entropy is related to Lloyd-Pagelsthermodynamic depth.]Gregory L. Eyink, "Action principle in nonequilbrium statisticaldynamics," Physical Review E 54 (1996):3419--3435K. H. Fischer and J. A. Hertz, Spin GlassesPierre Gaspard, Chaos, Scattering and StatisticalMechanicsA. Greven, G. Keller and G. Warnecke (eds.), EntropyGiovanni Jona-Lasinio, "From fluctuations in hydrodynamics tononequilibriumthermodynamics", arxiv:1003.4164Rolf Landauer, "Motion Out of NoisyStates," Journal ofStatistical Physics 53 (1988): 233--248 ["Therelative occupation of competing states of local stability is not determinedsolely by the characteristics of the locally favored states, but depends on thenoise along the whole path connecting the competing states. This is not new,but the sophistication of most modern treatments has obscured the simplicity ofthis central point, and here it is argued for in simple physical terms."]Michael Mackey, Time's Arrow: The Origin of ThermodynamicBehavior [This is a very valuable short introduction to theergodic theory of Markov operators, which ishighly relevant to the origins of irreversibility, etc., but I don't think hisapproach works, because he focuses on the relative entropy(Kullback-Leibler divergence from the invariant distribution), rather than theBoltzmann entropy or even the Gibbs entropy.]Mark Millonas (ed.), Fluctuations and Order: The NewSynthesis [Despite the subtitle, no synthesis is in evidence. However,many of the individual papers are very interesting.]Eric Smith, "Thermodynamic dual structure of linear-dissipativedriven systems", PhysicalReview E 72 (2005): 036130Hyung-June Woo, "Statistics of nonequilibrium trajectories andpatternselection", EurophysicsLetters 64 (2003): 627--633R. K. P. Zia, L. B. Shaw, B. Schmittmann and R. J. Astalos,"Contrasts Between Equilibrium and Non-Equilibrium Steady States: ComputerAided Discoveries in Simple Lattice Gases," cond-mat/9906376Modesty forbids me to recommend:CRS and Cristopher Moore, "What Is a Macrostate? SubjectiveMeasurements and Objective Dynamics,"cond-mat/03003625To read:D. Abreu, U. Seifert, "Thermodynamics of genuine non-equilibrium states under feedback control", arxiv:1109.5892Tameem Albash, Daniel A. Lidar, Milad Marvian, and Paolo Zanardi, "Fluctuation theorems for quantum processes", Physical Review E 88 (2013): 032146D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, andA. Petrosyan, "Entropy Production and Time Asymmetry in NonequilibriumFluctuations", Physical ReviewLetters98 (2007): 150601Francis J. Alexander and Gregory L. Eyink, "Rayleigh-RitzCalculation of Effective Potential Far from Equilibrium," Physical ReviewLetters 78 (1997): 1--4Bidhan Chandra Bag"Nonequilibrium stochastic processes: Time dependence ofentropy flux and entropy production," cond-mat/0205500"Upper bound for the time derivative of entropy fornonequilibrium stochastic processes," cond-mat/0201434BCB, Suman Kumar Banik, and Deb Shankar Ray, "The noiseproperties of stochastic processes and entropy production," cond-mat/0104524M. M. Bandi, W. I. Goldburg, J. R. Cressman Jr, "Measurement ofentropy production rate in compressibleturbulence", nlin.CD/0607036Julien Barre', Freddy Bouchet, Thierry Dauxois, Stefano Ruffo,"Out-of-equilibrium states as statistical equilibria of an effective dynamics,"cond-mat/0204407Daniel A. Beard and Hong Qian, "Relationship between ThermodynamicDriving Force and One-Way Fluxes in Reversible Chemical Reactions", q-bio.SC/0607020Christian Beck"Superstatistics in hydrodynamic turbulence,"physics/0303061"Superstatistics: Theory and Applications,"cond-mat/0303288Eric Bertin, Kirsten Martens, Olivier Dauchot, and Michel Droz,"Intensive thermodynamic parameters in nonequilibrium systems",Physical ReviewE75 (2007): 031120Eric Bertin, Olivier Dauchot, Michel Droz, "Definition andrelevance of nonequilibrium intensive thermodynamicparameters", PhysicalReview Letters 96 (2006):120601, cond-mat/0512116L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim"Current Fluctations in Stochastic Lattice Gases",Physical ReviewLetters 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/0602557Richard A. Blythe, "An introduction to phase transitions instochastic dynamicalsystems", cond-mat/0511627Doriano Brogioli, "Marginally Stable Chemical Systems as PrecursorsofLife", PhysicalReview Letters105 (2010): 058102Stephen G. Brush, The Kind of Motion We Call Heat:Statistical Physics and Irreversible ProcessesA. A. Budini and M.O. Caceres, "Functional characterization ofgeneralized Langevin equations", cond-mat/0402311 [Abstract:"We present an exact functional formalism to deal with linear Langevinequations with arbitrary memory kernels and driven by any noise structurecharacterized through its characteristic functional. No others hypothesis areassumed over the noise, neither the fluctuation dissipation theorem. We foundthat the characteristic functional of the linear process can be expressed interms of noise's functional and the Green function of the deterministic(memory-like) dissipative dynamics. This object allow us to get a procedure tocalculate all the Kolmogorov hierarchy of the non-Markov process. As exampleswe have characterized through the 1-time probability a noise-induced interplaybetween the dissipative dynamics and the structure of different noises.Conditions that lead to non-Gaussian statistics and distributions with longtails are analyzed. The introduction of arbitrary fluctuations in fractionalLangevin equations have also been pointed out."]Giovanni Bussi, Alessandro Laio and Michele Parrinello,"Equilibrium Free Energies from Nonequilibrium Metadynamics",Physical ReviewLetters 96 (2006): 090601C. Bustamante, J. Liphardt, and F. Ritort, "The NonequilibriumThermodynamics of Small Systems", PhysicsToday 58 (2005): 43--48,cond-mat/0511629Pasquale Calabrese and Andrea Gambassi, "On the definition of aunique effective temperature for non-equilibrium critical systems", cond-mat/0406289T. Carlsson, L. Sjogren, E. Mamontov, and K. Psiuk-Maksymowicz,"Irreducible memory function and slow dynamics in disordered systems",Physical ReviewE 75 (2007): 031109M. E. Cates and M. R. Evans (eds.), Soft and FragileMatter: Nonequilibrium Dynamics, Metastability and FlowPhilippe Chomaz, Francesca Gulminelli and Olivier Juillet,"Generalized Gibbs ensembles for time dependent processes", cond-mat/0412475E. G. D. Cohen, "Properties of nonequilibrium steady states: a pathintegralapproach", Journalof Statistical Mechanics (2008): P07014Leonardo Crochik and Tania Tome, "Entropy production in themajority-vote model", PhysicalReview E 72 (2005): 057103Daan Crommelin, "Estimation of Space-Dependent Diffusions and Potential Landscapes from Non-equilibrium Data", Journal of Statistical Physics 149 (2012): 220--233Gavin E. Crooks, "Measuring Thermodynamic Length",Physical ReviewLetters 99 (2007): 100602,arxiv:0706.0559 ["Thermodynamiclength is a metric distance between equilibrium thermodynamic states. Amongother interesting properties, this metric asymptotically bounds the dissipationinduced by a finite time transformation of a thermodynamic system. It is alsoconnected to the Jensen-Shannon divergence, Fisher information, and Rao'sentropy differential metric."]Gregory Bulnes Cuetara, Massimiliano Esposito, Alberto Imparato, "Exact fluctuation theorem without ensemble quantities", arxiv:1402.1873B. Derrida, "Non equilibrium steady states: fluctuations and largedeviations of the density and of thecurrent", cond-mat/0703762B. Derrida, Joel L. Lebowitz and Eugene R. Speer, "Exact LargeDeviation Functional for the Density Profile in a Stationary NonequilibriumOpen System," cond-mat/0105110Deepak Dhar, "Pico-canonical ensembles: A theoretical descriptionof metastable states," cond-mat/0205011math-ph/0304043Andreas Eibeck and Wolfgang Wagner, "Stochastic InteractingParticle Systems and Nonlinear KineticEquations", Annals ofApplied Probability 13 (2003): 845--889Vlad Elgart and Alex Kamenev, "Rare Events Statistics inReaction--Diffusion Systems", cond-mat/0404241 [i.e., largedeviations]Denis J. Evans and Gary Morriss, Statistical Mechanics of Nonequilibrium LiquidsR. M. L. Evans"Detailed balance has a counterpart in non-equilibriumsteady states", cond-mat/0408614"Rules for transition rates in nonequilibrium steadystates", cond-mat/0402527Massimo Falcioni, Luigi Palatella, Simone Pigolotti, LambertoRondoni and Angelo Vulpiani, "Boltzmann entropy and chaos in a large assemblyof weakly interacting systems", nlin.CD/0507038Gregory Falkovich and Alexander Fouxon, "Entropy production awayfrom equilibrium", nlin.CD/0312033 ["we expressthe entropy production via a two-point correlation function... the long-timelimit gives the sum of the Lyapunov exponents"]Roger Filliger and Max-Olivier Hongler, "Relative entropy andefficiency measure for diffusion-mediated transport processes", Journal of Physics A:Mathematical and General 38 (2005): 1247--1255 Silvio Franz, "How glasses explore configuration space,"cond-mat/0212091Henryk Fuks and Nino Boccara, "Convergence to equilibrium in aclass of interacting particle systems evolving in discrete time," nlin.CG/0101037Giovanni Gallavotti"Entropy creation in nonequilibriumthermodynamics: a review", cond-mat/0312657"Stationary nonequilibrium statisticalmechanics", cond-mat/0510027"Fluctuation relation, fluctuation theorem, thermostats andentropy creation in non equilibrium statisticalPhysics", cond-mat/0612061J. Galvao Ramos, Aurea R. Vasconcellos and Roberto Luzzi,"Nonlinear Higher-Order Thermo-Hydrodynamics II: Illustrative Examples", cond-mat/0412231Pierre Gaspard, The Statistical Mechanics of Irreversible PhenomenaPiotr Garbaczewski"Information Entropy Balance and Local MomentumConservation Laws in Nonequilibrium Random Dynamics," cond-mat/0301044"Shannon versus Kullback-Leibler Entropies inNonequilibrium Random Motion", cond-mat/0504115Nicolas B. Garnier and Daniel K. Wojcik, "Spatiotemporal Chaos: TheMicroscopic Perspective", Physical ReviewLetters 96 (2006): 114101Pierre Gaspard, "Time-Reversed Dynamical Entropy andIrreversibility in Markovian Random Processes", Journal of StatisticalPhysics 117 (2004): 599--615T. Gilbert, J. R. Dorfman and P. Gaspard, "Entropy Production,Fractals, and Relaxation to Equilibrium," Physical Review Letters85 (2000): 1606--1609S. Goldstein and J. L. Lebowitz, "On the (Boltzmann) Entropy ofNonequilibrium Systems,"cond-mat/0304251S. Goldsten, J. L. Lebowitz and Y. Sinai, "Remark on the(Non)convergence of Ensemble Densities in Dynamical Systems," math-ph/9804016Giacomo Gradenigo, Alessandro Sarracino, Andrea Puglisi, Hugo Touchette, "Fluctuation relations without uniform large deviations", Journal of Physics A 46 (2013): 335002, arxiv:1303.2851T. Hanney and R. B. Stinchcombe, "Real-space renormalisation groupapproach to driven diffusivesystems", cond-mat/0606515R. J. Harris, A. Rákos, G. M. Schuetz, "Breakdown ofGallavotti-Cohen symmetry for stochasticdynamics", cond-mat/0512159Hisao Hayakawa and Michio Otsuki, "Nonequilibrium identities and response theory for dissipative particles", Physical Review E 88 (2013): 032117Kumiko Hayashi and Hiroaki Takagi, "Fluctuation Thoerem appliedto Dictyostelium discoideum system", Journal of the PhysicalSociety of Japan 10 (2007): 105001, arxiv:0710.0523Kumiko Hayashi, Hiroshi Ueno, Ryota Iino, and Hiroyuki Noji,"Fluctuation Theorem Applied to F1-ATPase", PhysicalReview Letters 104 (2010): 218103Malte Henkel, "Ageing, dynamical scaling and its extensions inmany-particle systems without detailedbalance", cond-mat/0609672Haye Hinrichsen, "Critical Phenomena in Nonequilibrium Systems,"cond-mat/0001070Steven Huntsman, "Effective statistical physics of Anosov systems",arxiv:1009.2127Pablo I. Hurtado, Carlos Pérez-Espigares, Jesús J. del Pozo, and Pedro L. Garrido, "Symmetries in fluctuations far from equilibrium",Proceedings of the National Academyof Sciences (USA) 108 (2011): 7704--7709A. Imparato and L. Peliti"Work probability distribution insystems driven out of equilibrium", cond-mat/0507080"The distribution function of entropy flow in stochastic systems", cond-mat/0611078Claude Itzykson and Jean-Michel Drouffe, Statistical FieldTheory (2 vols.)M. V. Ivanchenko, O. I. Kanakov, V. D. Shalfeev and S. Flach,"Discrete breathers in transient processes and thermalequilibrium", Physica D 198 (2004): 120--135Dominik Janzing, "On the Entropy Production of Time Series withUnidirectionalLinearity", Journalof Statistical Physics 138 (2010): 767--779 [Open access]Christopher Jarzynski, "Comparison of far-from-equilibrium workrelations", cond-mat/0612305Owen Jepps, Denis J. Evans and Debra J. Searles, "The fluctuationtheorem and Lyapunov weights," cond-mat/0311090Alex Kamenev, Field Theory of Non-Equilibrium SystemsDragi Karevski, "Foundations of Statistical Mechanics: in and outof Equilibrium", cond-mat/0509595Kyogo Kawaguchi and Yohei Nakayama, "Fluctuation theorem for hidden entropy production", Physical Review E 88 (2013): 022147R. Kawai, J. M. R. Parrondo, C. Van den Broeck, "Dissipation: Thephase-spaceperspective", cond-mat/0701397Teruhisa S. Komatsu and Naoko Nakagawa, "Expression for theStationary Distribution in Nonequilibrium SteadyStates", Physical ReviewLetters 100 (2008): 030601Teruhisa S. Komatsu, Naoko Nakagawa, Shin-Ichi Sasa and Hal Tasaki,"Representation of Nonequilibrium Steady States in Large MechanicalSystems", Journalof Statistical Physics 134 (2009): 401--423Pavel L. Krapivsky, Sidney Redner and Eli Ben-Naim,A Kinetic View of Statistical PhysicsAnupam Kundu, "Nonequilibrium fluctuation theorem for systems under discrete and continuous feedback control", Physical Review E 86 (2012): 021107Jorge Kurchan, "Six out of equilibrium lectures",arxiv:0901.1271Michal Kurzynski, The Thermodynamic Machinery of LifeHernan Larralde, Francois Leyvraz, and David P. Sanders,"Metastability in Markov processes", Journalof Statistical Mechanics (2006): P08013, cond-mat/0608439Joel L. Lebowitz, "Boltzmann's Entropy and Large Deviation Lyapunov Functionals for Closed and Open Macroscopic Systems", arxiv:1112.1667Raphael Lefevere, "On the local space-time structure ofnon-equilibrium steady states", math-ph/0609049Dino Leporini and Roberto Mauri, "Fluctuations of non-conservative systems", Journal of Statistical Mechanics: Theory and Experiment 2007: P03002Francois Leyvraz, Hernan Larralde, and David P. Sanders, "ADefinition of Metastability for Markov Processes with DetailedBalance", cond-mat/0509754Katja Lindenberg and Bruce West, The NonequilibriumStatistical Mechanics of Open and Closed SystemsS. Lubeck, "Universal scaling behavior of non-equilibrium phasetransitions", 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:1302.1013James F. Lutsko, "Chapman-Enskog expansion about nonequilibriumstates: the sheared granularfluid", cond-mat/0510749Michael C. Mackey and Marta Tyran-Kaminska, "Temporal Behavior ofthe 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 whateveryone else calls "conditional entropy".]Christian Maes"Entropy Production in Driven Spatially ExtendedSystems," cond-mat/0101064"Elements of Nonequilibrium Statistical Mechanics"[PDF]"Statistical Mechanics of Entropy Production: Gibbsianhypothesis and local fluctuations," cond-mat/0106464Christian Maes and Karel Netocny"Time-Reversal and Entropy," cond-mat/0202501"Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states", arixv:0705.2344C. Maes, K. Netocny, B. Shergelashvili, "A selection ofnonequilibriumissues", math-ph/0701047[Lecture notes, 55 pp.]Christian Maes, Karel Netocny, Bram Wynants"On and beyond entropyproduction: the case of Markov jumpprocesses", 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 Letters107 (2011): 010601Christian Maes, Frank Redig and Michel Verschuere"From Global to Local Fluctuation Theorems," cond-mat/0106639"No current without heat," cond-mat/0111281Christian Maes, Hal Tasaki, "Second law of thermodynamics formacroscopic mechanics coupled to thermodynamic degrees offreedom", cond-mat/0511419Christian Maes and Maarten H. van Wieren, "Time-SymmetricFluctuations in Nonequilibrium Systems", Physical ReviewLetters 96 (2006): 240601,cond-mat/0601299Ferenc Markús and Katalin Gambár, "GeneralizedHamilton-Jacobi equation for simple dissipative processes", PhysicalReview E 70 (2004): 016123 [link]Joaquin Marro and Ronald Dickman, Nonequilibrium PhaseTransitions in Lattice ModelsDaniel C. Mattis and M. Larence Glasser, "The Uses of QuantumField Theory in Diffusion-Limited Reactions", Reviews of Modern Physics 70 (1998): 979--1001Paul Meakin, Fractals, Scaling and Growth Far fromEquilibriumS. S. Melnyk, O. V. Usatenko, and V. A. Yampol'skii, "MemoryFunctions of the Additive Markov chains: Applications to Complex DynamicSystems", physics/0412169Guillaume 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): 042102Emil Mittag and Denis J. Evans, "Time-dependent fluctuationtheorem," Physical Review E 67 (2003): 026113Geza 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 ConsistentFormulations of IrreversibleProcesses", Physical ReviewLetters 99 (2007): 130602Michele Pavon, "Stochastic control and nonequilibrium thermodynamical systems", Applied Mathematics and Optimiztion 19 (1989): 187--202Agusti Perez-Madrid, "Molecular Theory of Irreversibility",cond-mat/0509491Hans L. Pécseli, Fluctuations in PhysicalSystemsMark Pollicott and Richard Sharp, "Large Deviations, Fluctuations and Shrinking Intervals", Communicationsin Mathematical Physics 290 (2009): 321--334Noëlle Pottier, Nonequilibrium Statistical Physics:Linear Irreversible ProcessesHong Qian"A Gallavotti-Cohen-Type Symmetry in the Steady-stateKinetics of Single Enzyme Turnover Reactions", cond-mat/0507659"Relative Entropy: Free Energy Associated with EquilibriumFluctuations and NonequilibriumDeviations", math-ph/0007010= PhysicalReview E 63 (2001): 042103Hong Qian and Timothy C. Reluga, "Nonequilibrium Thermodynamics andNonlinear Kinetics in a Cellular Signaling Switch", Physical ReviewLetters 94 (2005): 028101Saar Rahav and Christopher Jarzynski, "Fluctuation relations andcoarse-graining", Journal of Statistical Mechanics (2007): P09012, arxiv:0708.2437 Jorgen Rammer, Quantum Field Theory of Non-equilibriumStatesJ. C. Reid, D. M. Carberry, G. M. Wang, E. M. Sevick, DenisJ. Evans and Debra J. Searles, "Reversibility in nonequilibrium trajectories ofan optically trapped particle", Physical ReviewE 70 (2004): 016111 [link]Pedro M. Reis, Rohit A. Ingale, Mark D. Shattuck, "Universalvelocity distributions in an experimental granularfluid", cond-mat/0611024[Measurable departures from the Maxwell-Boltzmann distribution, in accordancewith theory...]F. Ritort, "Single molecule experiments in biophysics: exploringthe thermal behavior of nonequilibrium smallsystems", cond-mat/0509606[Review]Edgar Roldan, Juan M.R. Parrondo, "Estimating dissipation from single stationary trajectories", arxiv:1004.2831L. Rondoni and E. G. D. Cohen, "Gibbs Entropy and IrreversibleThermodynamics," cond-mat/9908367Lamberto Rondoni, Carlos Mejia-Monasterio, "Fluctuations inNonequilibrium Statistical Mechanics: Models, Mathematical Theory, PhysicalMechanisms", arxiv:0709.1976David Ruelle"Extending the definition of entropy to nonequilibriumsteady states,"cond-mat/0303156"Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics", Proceedings of the National Academy of Sciences (USA) 109 (2012): 20344--20346Stefano Ruffo, "Equilibrium and nonequilibrium properties of systems with long-range interactions", European Physical Journal B 64 (2008): 355--363, arxiv:0711/1173Himadri S. Samanta and J. K. Bhattacharjee, "Non equilibriumstatistical physics with fictitioustime", cond-mat/0509563Shin-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:1306.4880Shin-ichi Sasa and Teruhisa S. Komats"Steady state thermodynamics", cond-mat/0411052[82pp. tome]"Thermodynamic Entropy and Excess Information Loss inDynamical Systems with Time-Dependent Hamiltonian," chao-dyn/9807010"Thermodynamic Irreversibility from High-DimensionlHamiltonian Chaos," cond-mat/9911181B. Schmittmann and R. K. P. Zia, Statistical Mechanics of Driven DiffusiveSystemsDebra 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 FluctuationTheorem," cond-mat/9906002Udo Seifert"Entropy production along a stochastic trajectory andan integral fluctuation theorem", cond-mat/0503686 = Physical ReviewLetters 95 (2005): 040602"Stochastic thermodynamics: principlesand perspectives", European Physical Journal B 64 (2008): 423--431, arxiv:0710.1187E.M. Sevick, R. Prabhakar, Stephen R. Williams, Debra J. Searles,"FluctuationTheorems", arxiv:0709.3888Geoffrey Sewell [Note to self: carefully compare these to papers byWoo]"On Connections between the Quantum and Hydrodynamical Pictures of Matter", arxiv:0710.1239"Quantum macrostatistical picture ofnonequilibrium steady states", math-ph/0403017"Quantum Macrostatistical Theory of Nonequilibrium SteadyStates", math-ph/0509069"Quantum Theory of Irreversibility: Open Systems andContinuum 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:1206.2750T. Speck and U. Seifert, "The Jarzynski relation, fluctuationtheorems, and stochastic thermodynamics for non-Markovianprocesses", Journal ofStatistical Mechanics (2007) L09002, arxiv:0709.2236Jaeyoung Sung, "Validity condition of the Jarzynski relation for aclassical mechanical system", cond-mat/0506214Tooru Taniguchi, E. G. D. Cohen, "Onsager-Machlup theory fornonequilibrium steady states and fluctuationtheorems", cond-mat/0605548=? Journalof Statistical Physics 130 (2007): 633--667Hal Tasaki"From Quantum Dynamics to the Second Law ofThermodynamics," cond-mat/0005128"The second law of Thermodynamics as a theorem in quantummechanics," cond-mat/0011321Uwe C. Tauber, "Field Theory Approaches to Nonequilibrium Dynamics",cond-mat/0511743C. Tietz, S. Schuler, T. Speck, U. Seifert, and J. Wrachtrup,"Measurement of Stochastic Entropy Production", Physical ReviewLetters 97 (2006): 050602= cond-mat/0607407Alexei V. Tkachenko, "Generalized Entropy Approach toFar-from-Equilibrium Statistical Mechanics," cond-mat/0005198H. Touchette and E. G. D. Cohen, "A novel fluctuation relation fora Lévyparticle", cond-mat/0703254=? Physical ReviewE76 (2007) 020101H. Touchette, M. Costeniuc, R.S. Ellis, and B. Turkington,"Metastability within the generalized canonicalensemble", cond-mat/0509802Hugo Touchette, Rosemary J. Harris, "Large deviation approach to nonequilibrium systems", arxiv:1110.5216E. H. Trepagnier, C. Jarzynski, F. Ritort, G. E. Crooks, C. J.Bustamante and J. Liphardt, "Experimental test of Hatano and Sasa'snonequilibrium steady-state equality", Proceedings of theNational 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:1207.2692Ramses van Zon, H. van Beijeren and J. R. Dorfman, "Kinetic Theoryof Dynamical Systems," chao-dyn/9906040Aurea R. Vasconcellos, J. Galvao Ramos and Roberto Luzzi,"Nonlinear Higher-Order Thermo-Hydrodynamics: Generalized Approach in aNonequilibrium Ensemble Formalism", cond-mat/0412227G. M. Wang, J. C. Reid, D. M. Carberry, D. R. M. Williams,E. M. Sevick, and Denis J. Evans, "Experimental study of the fluctuationtheorem in a nonequilibrium steady state", PRE 71(2005): 046142Stephen R. Williams, Debra J. Searles, Denis J. Evans, "Numericalstudy of the Steady State Fluctuation Relations Far fromEquilibrium", cond-mat/0601328Hyung-June Woo, "Variationalformulation of nonequilibrium thermodynamics for hydrodynamic patternformations," Physical Review E 66 (2002) 066104Jeroen 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:1208.3080Bram Wynants, "Structures of nonequilibrium fluctuations: dissipation and activity", arxiv:1011.4210V. I. Yukalov, "Principle of Pattern Selection for NonequilibriumPhenomena,"cond-mat/0110107Francesco Zamponi, "Is it possible to experimentally verify thefluctuation relation? A review of theoretical motivations and numericalevidence", cond-mat/0612019Juan Zanella and Esteban Calzetta, "Renormalization group andnonequilibrium action in stochastic field theory,"Physical ReviewE 66 (2002): 036134H. D. Zeh, Physical Basis of the Direction of TimeR. K. P. Zia, B. Schmittmann, "A possible classification ofnonequilibrium steadystates", cond-mat/0605301D. N. Zubarev et al., Statistical Mechanics of NonequilibriumProcessesRobert Zwanzig, Nonequilibrium Statistical MechanicsTo write someday, when I'd understand it:"Variational Principles in Nonequilibrium Statistical Mechanics"
Honerkamp Stochastic Dynamical Systems Pdf Free
2ff7e9595c
Comments