Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

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

doi:10.1088/1742-5468/2007/07/p07012

Cited by 230 publications

(314 citation statements)

References 76 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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“…T mn = 32,57,58 in both discrete and continuous case. The detailed balance part of the driving force is largely dependent on the diagonal element of the density matrix: the steady state population.…”

Section: General Theoretical Framework For Non-equilibrium Quantumentioning

confidence: 99%

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

Zhang

Wang

2014

The Journal of Chemical Physics

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We established a theoretical framework in terms of the curl flux, population landscape and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of nonequilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunnelling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunnelling strength, the quantum flux is promoted by the coherence in the regime of small tunnelling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the nonequilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency (ETE or CTE), chemical reaction efficiency (CRE), energy dissipation, heat and electric currents observed in the experiments. We observed a perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference). Our theoretical predicted behavior of the electric current with respect to the voltage is in good agreements with the recent experiments on electron transfer in single molecules.

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Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

Cited by 230 publications

References 76 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

Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics

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