Universal theory of efficiency fluctuations

Verley, Gatien; Willaert, Tim; Broeck, C. Van den; Esposito, Massimiliano

doi:10.1103/physreve.90.052145

Cited by 122 publications

(206 citation statements)

References 44 publications

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“…In contrast to Refs. [45,46], the phase space is found to be continuous with infinite microstates, and it has been shown that the large deviation function does not follow the universal nature as mentioned in Refs. [45,46].…”

Section: Introductionmentioning

confidence: 94%

“…Moreover, the large deviation function has two extrema: a maximum corresponds to the most probable efficiency, and the minimum occurs at Carnot efficiency. In a similar context, Verley et al [46], found an efficient way to compute the large deviation function of stochastic efficiency using the cumulant generating function of entropy productions for a small engine with finite state space. This method was verified by considering an example of a stochastic engine made up of a system of two states where each of these states is coupled to a heat reservoir at a distinct temperature.…”

Section: Introductionmentioning

confidence: 99%

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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: 94%

Section: Introductionmentioning

confidence: 99%

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

Gupta

Sabhapandit

2017

Phys. Rev. E

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“…The ratio of these variables yields the efficiency which is thus itself random variable. Large deviation form of the corresponding probability distribution exhibits the following universal features [40][41][42][43][44][45][46][47][48]: (i) the most probable value of efficiency corresponds to its traditional definition using averages of work and heat, (ii) in case of time-reversal symmetric driving the least probable value of efficiency equals to η C .…”

Section: Introductionmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.

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“…The non self-averaging nature of fluctuations in stochastic efficiency and other quantities requires detailed understanding of full probability distributions as opposed to the average behavior [41,42]. Large deviation properties of such distributions are recently under theoretical investigations [45,46,47,48,49,50,51]. Research on fluctuation relations for heat engines [52,53,54] are being pursued.…”

Section: Introductionmentioning

confidence: 99%

“…However, fluctuation theorems provide a bound on efficiency of an engine valid for any finite time cycle. Recently, novel theoretical approaches to capture the statistical properties of stochastic efficiency of micro heat engines and mesoscopic thermoelectric engines with broken time-reversal symmetry are being developed, particularly at long time limit [43,44], claiming universal properties of the large deviation function related to the statistics of stochastic efficiency. To our knowledge, so far, no such study exists for micro-refrigerators.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Brownian refrigerator

Rana

Pal

Saha

et al. 2016

Physica A: Statistical Mechanics and its Applications

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We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

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Universal theory of efficiency fluctuations

Cited by 122 publications

References 44 publications

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

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

Efficiency at and near maximum power of low-dissipation heat engines

Anomalous Brownian refrigerator

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