Fluctuation theorem for entropy production of a partial system in the weak-coupling limit

Gupta, Deepak; Sabhapandit, Sanjib

doi:10.1209/0295-5075/115/60003

Cited by 13 publications

(30 citation statements)

References 49 publications

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“…When such small-scale machines are driven by external forces, like temperature or concentration gradient, shear flow, time-dependent external field, etc., observables such as work done, heat flow, power injection, entropy production, etc., become stochastic quantities [18][19][20][21][22][23][24][25][26][27][28][29][30]. The probability distributions of these quantities have richer information than their ensemble average values.…”

Section: Introductionmentioning

confidence: 99%

Stochastic efficiency of an isothermal work-to-work converter engine

Gupta

Sabhapandit

2017

Phys. Rev. E

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We investigate the efficiency of an isothermal Brownian work-to-work converter engine, composed of a Brownian particle coupled to a heat bath at a constant temperature. The system is maintained out of equilibrium by using two external time-dependent stochastic Gaussian forces, where one is called load force and the other is called drive force. Work done by these two forces are stochastic quantities. The efficiency of this small engine is defined as the ratio of stochastic work done against load force to stochastic work done by the drive force. The probability density function as well as large deviation function of the stochastic efficiency are studied analytically and verified by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Stochastic efficiency of an isothermal work-to-work converter engine

Gupta

Sabhapandit

2017

Phys. Rev. E

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“…Proof. Let us construct the tilted generator of the forward and backward dynamics in terms of the Hadamard product (see p. 19) as (we drop the explicit range of the indices)…”

Section: Fluctuation Relationsmentioning

confidence: 99%

Effective Fluctuation and Response Theory

Polettini

Esposito

2019

J Stat Phys

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The response of thermodynamic systems slightly perturbed out of an equilibrium steady-state is described by two milestones of early nonequilibrium statistical mechanics: the reciprocal and the fluctuation-dissipation relations. At the turn of this century, the so-called fluctuation theorems extended the study of fluctuations far beyond equilibrium. All these results rely on the crucial assumption that the observer has complete information about the system: there is no hidden leakage to the environment, and every process is assigned its due thermodynamic cost. Such a precise control is difficult to attain, hence the following questions are compelling: Will an observer who has marginal information be able to perform an effective thermodynamic analysis? Given that such observer will only be able to establish local equilibrium amidst the whirling of hidden degrees of freedom, by perturbing the stalling currents will he/she observe equilibrium-like fluctuations nevertheless? We address these two fundamental problems, providing a broad theory of the statistical behavior of some out of many currents that flow across a thermodynamic system.We model the dynamics of open systems as Markov jump processes on finite networks. Configurationspace currents count the net number of transitions between pairs of configurations; conjugate forces quantify their thermodynamic cost. Phenomenological currents are linear combinations of configuration currents, and only ensue when affinities enjoy appropriate symmetries, granting thermodynamic consistency. A complete thermodynamic description is achieved when the set of currents under consideration covers all cycles in the network, otherwise the set is marginal.Within this formalism, we establish that: 1) While marginal currents do not obey a full-fledged fluctuation relation, there exist effective affinities for which an integral fluctuation relation holds; 2) Under reasonable assumptions on the parametrization of the rates, effective and "real" affinities only differ by a constant; 3) At stalling, i.e. where the marginal currents vanish, a symmetrized fluctuation-dissipation relation holds while reciprocity does not; 4) There exists a notion of marginal time-reversal that plays a role akin to that played by time-reversal for complete systems, which restores the fluctuation relation and reciprocity; 5) The effective affinity is the putative affinity of an observer who only has marginal information about a system and formulates a minimal model accounting for his/her steady-state observations; 6) There exist fluctuation relations across different levels in the hierarchy of more and more "complete" theories. The above results hold for configurationspace currents, and for phenomenological currents provided that certain symmetries of the effective affinities are respected -a condition that we call marginal thermodynamic consistency, which is stricter thermodynamic consistency and whose range of validity we deem the most interesting question left open to future inquiry. Our results are construc...

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“…The term g 0 (λ) is the same prefactor term as given in (92). The term g 1 (λ) may have singularities, but in the limit δ → 0, we can approximate the correction term as [43,44] g(λ) ≈ g 0 (λ). Computation of the integral given in (68), is quite involved and not very illuminating to us.…”

Section: Probability Distribution Functionmentioning

confidence: 99%

Partial entropy production in heat transport

Gupta

Sabhapandit

2018

J. Stat. Mech.

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We consider a system of two Brownian particles (say A and B), coupled to each other via harmonic potential of stiffness constant k. Particle-A is connected to two heat baths of constant temperatures T 1 and T 2 , and particle-B is connected to a single heat bath of a constant temperature T 3 . In the steady state, the total entropy production for both particles obeys the fluctuation theorem. We compute the total entropy production due to one of the particles called as partial or apparent entropy production, in the steady state for a time segment τ . When both particles are weakly interacting with each other, the fluctuation theorem for partial and apparent entropy production is studied. We find a significant deviation from the fluctuation theorem. The analytical results are also verified using numerical simulations.

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Fluctuation theorem for entropy production of a partial system in the weak-coupling limit

Cited by 13 publications

References 49 publications

Stochastic efficiency of an isothermal work-to-work converter engine

Stochastic efficiency of an isothermal work-to-work converter engine

Effective Fluctuation and Response Theory

Partial entropy production in heat transport

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