Notebooks

## Nonequilibrium Statistcal Mechanics and Thermodynamics

24 Jul 2023 22:17

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.

*: Pedantically, a Gibbs distribution over a collection of variables $X_t$, index by $\mathcal{T}$, collectively $X$, will take the form $\mathbb{P}(X=x) \propto e^{-u(x)}$, and the "potential" $u(x) = \sum_{A \in 2^{\mathcal{T}}}{u_A(x_A)}$, 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.

• Fluctuation-Response Relations
• Foundations 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-Equilibrium Thermodynamics
• J. R. Dorfman, Introduction to Chaos in Nonequilibrium Statistical Mechanics
• 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!]
• Josef Honerkamp, Stochastic Dynamical Systems
• Joel Keizer, Statistical Thermodynamics of Nonequilibrium Processes [Review: Molecular Fluctuations for Fun and Profit]
• 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, "Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions", arxiv:1102.3938
• Hugo Touchette, "The Large Deviations Approach to Statistical Mechanics", Physics Reports 478 (2009): 1--69, arxiv:0804.0327
Recommended, close-ups:
• 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
• 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."]
• 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
• Pierre Gaspard, Chaos, Scattering and Statistical Mechanics
• A. Greven, G. Keller and G. Warnecke (eds.), Entropy
• Giovanni Jona-Lasinio, "From fluctuations in hydrodynamics to nonequilibrium thermodynamics", arxiv:1003.4164
• 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.]
• Eric Smith, "Thermodynamic dual structure of linear-dissipative driven systems", Physical Review E 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
• D. Abreu, U. Seifert, "Thermodynamics of genuine non-equilibrium states under feedback control", arxiv:1109.5892
• Anthony Aguirre, Sean M. Carroll, Matthew C. Johnson, "Out of equilibrium: understanding cosmological evolution to lower-entropy states", arxiv:1108.0417
• 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, 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
• 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
• 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
• 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 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
• 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
• Pierre Gaspard, The Statistical Mechanics of Irreversible Phenomena
• 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", Journal of Statistical Mechanics (2006): P08013, cond-mat/0608439
• 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
• Christian Maes, Frank Redig and Michel Verschuere
• 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
• 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
• Michele Pavon, "Stochastic control and nonequilibrium thermodynamical systems", Applied Mathematics and Optimiztion 19 (1989): 187--202
• 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
• Hong Qian
• 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", Journal of Statistical Mechanics (2007): P09012, arxiv:0708.2437
• 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
• 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
• 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
• Udo Seifert
• 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
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• H. D. Zeh, Physical Basis of the Direction of Time
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• Robert Zwanzig, Nonequilibrium Statistical Mechanics
To write someday, when I'd understand it:
• "Variational Principles in Nonequilibrium Statistical Mechanics"