Fluctuation theorem for the effusion of an ideal gas

Cleuren, Bart; Broeck, C. Van den; Kawai, Ryoichi

doi:10.1103/physreve.74.021117

Cited by 52 publications

(58 citation statements)

References 38 publications

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“…The results here reported have important applications for the nonlinear response properties of many nonequilibrium systems such as the chemical and biochemical reactions [13], the full counting statistics in mesoscopic conductors [15], the effusion of ideal gases [24], and Van den Broeck's demons [25]. The present results could be especially important in nonequilibrium systems at the micro-and nano-scales, where the nonlinear response properties turn out to be dominant [26].…”

Section: Discussionmentioning

confidence: 92%

A fluctuation theorem for currents and non-linear response coefficients

2007

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We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations.

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Section: Discussionmentioning

confidence: 92%

A fluctuation theorem for currents and non-linear response coefficients

2007

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“…Such a universality is remarkable in view of the fact that most explicit macroscopic relationships, for example the symmetry of Onsager coefficients, are limited to the regime of linear response. The interest in strong coupling is further motivated by the observation that it can naturally be achieved in nano-devices [10,11,12]. To complement our theoretical discussion, we also present a detailed study of a thermal nano-machine based on the operation of a maser [13].…”

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confidence: 99%

“…Here I is the current introduced in Eq. (12) and the associated thermodynamic force F can be expressed in terms of dimensionless scaled energies x l and x r ,…”

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confidence: 99%

Universality of Efficiency at Maximum Power

Esposito

Lindenberg²,

Broeck³

2009

Phys. Rev. Lett.

405

447

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We investigate the efficiency of power generation by thermo-chemical engines. For strong coupling between the particle and heat flows and in the presence of a left-right symmetry in the system, we demonstrate that the efficiency at maximum power displays universality up to quadratic order in the deviation from equilibrium. A maser model is presented to illustrate our argument. The concept of Carnot efficiency is a cornerstone of thermodynamics. It states that the efficiency of a cyclic ("Carnot") thermal engine that transforms an amount Q r of energy extracted from a heat reservoir at temperature T r into an amount of work W is at most η = W/Q r ≤ η c = 1 − T l /T r , where T l is the temperature of a second, colder reservoir. The theoretical implications of this result are momentous, as they lie at the basis of the introduction by Clausius of the entropy as a state function. The practical implications are more limited, since the upper limit η c ("Carnot efficiency") is only reached for engines that operate reversibly. As a result, when the efficiency is maximal, the output power is zero. By optimizing the Carnot cycle with respect to power rather than efficiency, Curzon and Ahlborn found that the corresponding efficiency is given by η CA = 1 − T l /T r [1]. They obtained this result for a specific model, using in addition the so-called endo-reversible approximation (i.e., neglecting the dissipation in the auxiliary, work producing entity). Subsequently, the validity of this result as an upper bound, as well as its universal character, were the subject of a longstanding debate. In the regime of linear response, more precisely to linear order in η c , it was proven that the efficiency at maximum power is indeed limited by the Curzon-Ahlborn efficiency, which in this regime is exactly half of the Carnot efficiency,. The upper limit is reached for a specific class of models, namely, those for which the heat flux is strongly coupled to the work-generating flux. Interestingly, such strong coupling is also a prerequisite for open systems to achieve Carnot efficiency [3,4]. In the nonlinear regime, no general result is known. Efficiencies at maximum power, not only below but also above Curzon-Ahlborn efficiency, have been reported [5,6,7,8]. However, it was also found, again in several strong coupling models [7,8,9], that the efficiency at maximum power agrees with η CA up to quadratic order in η c , i.e., η = η c /2+η 2 c /8+O(η 3 c ), again raising the question of universality at least to this order. In this letter we prove that the coefficient 1/8 is indeed universal for strong coupling models that possess a left-right symmetry. Such a universality is remarkable in view of the fact that most explicit macroscopic relationships, for example the symmetry of Onsager coefficients, are limited to the regime of linear response. The interest in strong coupling is further motivated by the observation that it can naturally be achieved in nano-devices [10,11,12]. To complement our theoretical discussion, we also present a deta...

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“…The past decade has brought new insights into nonequilibrium statistical mechanics due to the discovery of various types of fluctuation relations valid arbitrarily far from equilibrium [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. These relations identify, at the level of the single realization of a statistical ensemble, the "trajectory entropy" which upon ensemble averaging reproduce the thermodynamic entropy.…”

Section: Introductionmentioning

confidence: 99%

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

2007

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The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: an arbitrary nonequilibrium transformation always produces a change in the total entropy production greater or equal than the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.

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Fluctuation theorem for the effusion of an ideal gas

Abstract: The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

Cited by 52 publications

References 38 publications

A fluctuation theorem for currents and non-linear response coefficients

A fluctuation theorem for currents and non-linear response coefficients

Universality of Efficiency at Maximum Power

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

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