A possible classification of nonequilibrium steady states

Zia, R. K. P.; Schmittmann, Beate

doi:10.1088/0305-4470/39/24/l04

Cited by 78 publications

(83 citation statements)

References 9 publications

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“…It is worth noting that the behavior of the mean entropy production rate is similar to that of a quantity derived from the stationary probability currents [35][36][37] that has been proposed as a possible measure for the non-equilibrium character of a system. For example, both quantities show a non-monotonous change for model M ′ 2 when increasing h, whereas their increase is monotonous for models M 2 and M 3 (see Fig.…”

Section: B the Long Time Limitmentioning

confidence: 99%

Entropy production in the nonequilibrium steady states of interacting many-body systems

Dorosz

Pleimling

2011

Phys. Rev. E

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Entropy production is one of the most important characteristics of non-equilibrium steady states.We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of non-equilibrium systems: transport systems and reaction-diffusion systems. The usefulness of the mean entropy production rate and of the large deviation function of the entropy production for characterizing non-equilibrium steady states of interacting manybody systems is discussed. We show that the large deviation function displays a kink-like feature at zero entropy production that is similar to that observed for a single particle driven along a periodic potential. This kink is a direct consequence of the detailed fluctuation theorem fulfilled by the probability distribution of the entropy production and is therefore a generic feature of the corresponding large deviation function.

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Section: B the Long Time Limitmentioning

confidence: 99%

Entropy production in the nonequilibrium steady states of interacting many-body systems

Dorosz

Pleimling

2011

Phys. Rev. E

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“…Based on these observations and starting with the Langevin equation above, a field theoretic renormalization group analysis can be set up [31][32][33] and, unlike the Ising universality class [34], the upper critical dimension is d c = 5. More significantly, the fixed point cannot be written in terms of a "Hamiltonian" and is genuinely "non-equilibrium" in the sense that it contains a term corresponding to a non-trivial (probability) current [35,36]. By contrast, a similar treatment for the RDLG leads to a fixed point Hamiltonian [18,19], so that its leading singularities fall into the universality class of a system in equilibrium.…”

Section: The Driven Lattice Gas and Its Surprising Behaviormentioning

confidence: 99%

Twenty Five Years After KLS: A Celebration of Non-equilibrium Statistical Mechanics

Zia

2009

J Stat Phys

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When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. We present a brief review of some of the new insights garnered and some of the outstanding puzzles, as well as speculate on the model's role in the future of non-equilibrium statistical physics.

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“…of detailed balance, P * (C) exists and can still be constructed from the w's, though non-trivial [66,7]. Since the divergence of these currents must vanish, they must form 375 current loops.…”

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confidence: 99%

“…violating rates with IRLs [66,7]. Our proposal is that all stationary states should be 382 characterized by the pair {P * , K * }.…”

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confidence: 99%

Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport

Chou¹,

2011

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Abstract. Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a onedimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.

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A possible classification of nonequilibrium steady states

Cited by 78 publications

References 9 publications

Entropy production in the nonequilibrium steady states of interacting many-body systems

Entropy production in the nonequilibrium steady states of interacting many-body systems

Twenty Five Years After KLS: A Celebration of Non-equilibrium Statistical Mechanics

Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport

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