Work and power production in non-equilibrium systems

Gaveau, Bernard; Moreau, M.; Schulman, L. S.

doi:10.1016/j.physleta.2008.01.081

Cited by 8 publications

(10 citation statements)

References 18 publications

(19 reference statements)

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“…Here we follow a method similar to that used by Crooks [30,31] and by Gaveau et al [32]. We discretize the time in intervals ∆t so that ∆tW (η ′ |η) = T (η ′ |η) will be the transition probability from η to η ′ .…”

Section: E Jarzynski Equalitymentioning

confidence: 99%

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Entropy production in irreversible systems described by a Fokker-Planck equation

2010

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We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

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Section: E Jarzynski Equalitymentioning

confidence: 99%

“…We use the expressions (7) and (8) for the entropy flux and entropy production to determine an equality of the Jarzynski type [28][29][30][31][32]. This is carried out by considering the ratio of the probability of a given trajectory in phase space and the probability of the time reversal trajectory.…”

Section: Introductionmentioning

confidence: 99%

Entropy production in irreversible systems described by a Fokker-Planck equation

2010

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“…Hence this free energy difference has also been called an entropy deficiency [4]. Equivalently, if the system is coupled to a mechanical system, this free energy difference equals the maximum work that can be done on that mechanical system while the original system relaxes to equilibrium (also known as the exergy) [5,6].Interestingly, the free energy difference between two ensembles with identical values of the control parameter, one distributed among microstates according to the equilibrium probability distribution P eq λ (x) = exp{β [F eq λ − E λ (x)]} and one out of equilibrium and distributed according to P neq , is equal to the relative entropy D(P neq P eq λ ) ≡ x P neq (x) ln[P neq (x)/P eq λ (x)] between the two probability distributions [2]:…”

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confidence: 99%

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confidence: 99%

Near-Equilibrium Measurements of Nonequilibrium Free Energy

Sivak

Crooks

2012

Phys. Rev. Lett.

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A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a nonequilibrium ensemble is that it is larger than that of the same system at equilibrium. Herein, we derive a formally exact expression for the probability distribution of a driven system, which involves path ensemble averages of the work over trajectories of the time-reversed system. From this we find a simple near-equilibrium approximation for the free energy in terms of an excess mean time-reversed work, which can be experimentally measured on real systems. With analysis and computer simulation, we demonstrate the accuracy of our approximations for several simple models.

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“…For any function h of the system state x, we write δ xy h = h(x) − h(y). Thus δ xy s = s(x) − s(y), whereas (δS) xy is the entropy variation of the external systems: it is supposed to depend only on x and y, as discussed below, but in general it is not the variation from y to x of any function of the system state alone [1,2]. If, under special conditions, it happens that there is a function S tot (x) such that (δS tot ) xy = S tot (x) − S tot (y) for all (x, y), the only stationary distribution p 0 (x) of s is p 0 (x) ∝ S tot (x), and detailed balance [2,3,4,5,6] holds R xy p 0 (x) = R yx p 0 (y) ;…”

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confidence: 99%

Generalized Clausius relation and power dissipation in nonequilibrium stochastic systems

2009

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In the framework of the stochastic dynamics of open Markov systems, we derive an extension of the Clausius inequality for transitions between states of the system. We give a formula for the power produced when the system is in its stationary state and relate it to the dissipation of energy needed to maintain the system out of equilibrium. We deduce that, near equilibrium, maximal power production requires an energy dissipation of the same order of magnitude as the power production.

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Work and power production in non-equilibrium systems

Cited by 8 publications

References 18 publications

Entropy production in irreversible systems described by a Fokker-Planck equation

Entropy production in irreversible systems described by a Fokker-Planck equation

Near-Equilibrium Measurements of Nonequilibrium Free Energy

Generalized Clausius relation and power dissipation in nonequilibrium stochastic systems

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