A Nonequilibrium Extension of the Clausius Heat Theorem

Maes, Christian; Netočný, Karel

doi:10.1007/s10955-013-0822-9

Cited by 70 publications

(112 citation statements)

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“…Other schemes for SST, which are distinct from those in [2,3], have been proposed [9,10,11,13,14]. See the end of section 1.2 for details.…”

Section: Background and Motivationmentioning

confidence: 99%

“…A very close, but slightly different, scheme based on macroscopic fluctuation theory was recently proposed by Bertini, Gabrielli, Jona-Lasinio, and Landim [10,11]. The scheme due to Maes and Netocny [13] makes a full use of the large deviation analysis. See [13,14] for discussions about the relations between different schemes.…”

Section: Extended Clausius Relationmentioning

confidence: 99%

“…The scheme due to Maes and Netocny [13] makes a full use of the large deviation analysis. See [13,14] for discussions about the relations between different schemes.…”

Section: Extended Clausius Relationmentioning

confidence: 99%

“…Entropy production: For any x, y ∈ S such that R α x→y = 0, we define the entropy production in the heat baths 8 associated with the transition x → y by 13) or, equivalently, by the "local detailed balance condition"…”

Section: Entropy Production Work and Time-reversalmentioning

confidence: 99%

“…It then turns out (see (2.36)) that Ψα[x] is identical to β times the total work done to the system by the external field. The work done by the external field may be measured in principle 13 , but the measurement seems to be extremely difficult in general. We thus regard Ψα[x] as a semi-measurable quantity in this case.…”

Section: Entropy Production Work and Time-reversalmentioning

confidence: 99%

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Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States

et al. 2015

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We study thermodynamic operations which bring a nonequilibrium steady state (NESS) to another NESS in physical systems under nonequilibrium conditions. We model the system by a suitable Markov jump process, and treat thermodynamic operations as protocols according to which the external agent varies parameters of the Markov process. Then we prove, among other relations, a NESS version of the Jarzynski equality and the extended Clausius relation. The latter can be a starting point of thermodynamics for NESS. We also find that the corresponding nonequilibrium entropy has a microscopic representation in terms of symmetrized Shannon entropy in systems where the microscopic description of states involves "momenta". All the results in the present paper are mathematically rigorous.

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“…Other schemes for SST, which are distinct from those in [2,3], have been proposed [9,10,11,13,14]. See the end of section 1.2 for details.…”

Section: Background and Motivationmentioning

confidence: 99%

Section: Extended Clausius Relationmentioning

confidence: 99%

“…The scheme due to Maes and Netocny [13] makes a full use of the large deviation analysis. See [13,14] for discussions about the relations between different schemes.…”

Section: Extended Clausius Relationmentioning

confidence: 99%

Section: Entropy Production Work and Time-reversalmentioning

confidence: 99%

Section: Entropy Production Work and Time-reversalmentioning

confidence: 99%

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Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States

et al. 2015

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Basics of Stochastic Thermodynamics

Ryabov

2015

Springer Theses

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Equivalent Definitions of the Quantum Nonadiabatic Entropy Production

Horowitz

Sagawa

2014

J Stat Phys

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The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy production have appeared in the literature, one based on the quantum relative entropy and the other based on quantum trajectories. We show that these two formulations are equivalent. Furthermore, this equivalence leads us to a proof of the monotonicity of the quantum relative entropy under a special class of completely-positive, trace-preserving quantum maps, which circumvents difficulties associated with the noncommuntative structure of operators.Keywords Quantum nonequilibrium thermodynamics · Nonadiabatic entropy production · Quantum relative entropy monotonicity IntroductionA diversity of physical systems are prevented from relaxing to thermodynamic equilibrium by nonconservative forces or nonequilibrium boundary conditions. Instead, they are maintained in a nonequilibrium steady state characterized by continuously dissipating currents [1,2,3]. As thermodynamic systems, the second law of thermodynamics requires their entropy production rate to always be positive,Ṡ tot ≥ 0. Unfortunately, this inequality is uninformative for driven transitions between distinct nonequilibrium steady states,

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A Nonequilibrium Extension of the Clausius Heat Theorem

Abstract: We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact

Cited by 70 publications

References 22 publications

Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States

Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States

Basics of Stochastic Thermodynamics

Equivalent Definitions of the Quantum Nonadiabatic Entropy Production

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