Affinity- and topology-dependent bound on current fluctuations

Pietzonka, Patrick; Barato, Andre C.; Seifert, Udo

doi:10.1088/1751-8113/49/34/34lt01

Cited by 44 publications

(54 citation statements)

References 22 publications

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“…While empirical currents are the natural trajectory observables to consider in driven problems [1][2][3][4][5]29,30,33,35,36,40], counting observables such as the dynamical activity are central quantities for systems with complex equilibrium dynamics, such as glass formers [24,25,42,43,46]. (And even for driven systems it is revealing to study the dynamical phase behavior in terms of both empirical currents and activities; see e.g.…”

Section: Discussionmentioning

confidence: 99%

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Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

2017

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Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

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Section: Discussionmentioning

confidence: 99%

“…As occurs with the analogous bounds on time-integrated currents [1][2][3][4], an immediate consequence of the bounds on the rate function or cumulant generating function are the thermodynamic uncertainty relations [13][14][15]. From Eq.…”

Section: Level 25 and Fluctuation Boundsmentioning

confidence: 99%

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

2017

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“…The time-independent parameters K ij are anti-symmetric, i.e., K ij =−K ji , and satisfy å = ¹ ( ) K 0, 51 j i ij for all states i. Using this choice in equation (47), we obtain , where * s is defined in equation (20). For currents with time-independent increments α ij (t)=α ij , we obtain…”

Section: First Global Boundmentioning

confidence: 99%

“…A key feature of this parabolic bound is that it depends solely on the average entropy production and the average current, i.e., knowledge of the average entropy production and the average current implies a bound on arbitrary fluctuations of any thermodynamic current. There has been much recent work related to this universal principle about current fluctuations [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Bounds on current fluctuations in periodically driven systems

et al. 2018

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Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem. More recently, it has been found that, for nonequilibrium stationary states, the full spectrum of fluctuations of any thermodynamic current is bounded by the average rate of entropy production and the average current. However, this bound does not apply to periodically driven systems, such as heat engines driven by periodic variation of the temperature and artificial molecular pumps driven by an external protocol. We obtain a universal bound on current fluctuations for periodically driven systems. This bound is a generalization of the known bound for stationary states. In general, the average rate that bounds fluctuations in periodically driven systems is different from the rate of entropy production. We also obtain a local bound on fluctuations that leads to a trade-off relation between speed and precision in periodically driven systems, which constitutes a generalization to periodically driven systems of the so called thermodynamic uncertainty relation. From a technical perspective, our results are obtained with the use of a recently developed theory for 2.5 large deviations for Markov jump processes with time-periodic transition rates.

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“…Several works about the TUR and quadratic bounds on LD rate functionals have already been produced (see for example [1, 2, 8, 9, 10, 11, 12, 13, 16, 19, 20, 23, This work has been supported by Italian PRIN 20155PAWZB "Large Scale Random Structures" and by the project "Investissements d'Avenir" UCA JEDI of the French ANR n. ANR-15-IDEX-01. 24,26,27,28,29,32,33,34,36,37,38,39,40,41,42] and references therein). In particular, the TUR applies to systems driven by a fixed thermodynamic force.…”

Section: Introductionmentioning

confidence: 99%

A unifying picture of generalized thermodynamic uncertainty relations

Barato¹,

Chétrite²,

Faggionato³

et al. 2019

J. Stat. Mech.

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The thermodynamic uncertainty relation is a universal trade-off relation connecting the precision of a current with the average dissipation at large times. For continuous time Markov chains (also called Markov jump processes) this relation is valid in the time-homogeneous case, while it fails in the timeperiodic case. The latter is relevant for the study of several small thermodynamic systems. We consider here a time-periodic Markov chain with continuous time and a broad class of functionals of stochastic trajectories, which are general linear combinations of the empirical flow and the empirical density. Inspired by the analysis done in our previous work [1], we provide general methods to get local quadratic bounds for large deviations, which lead to universal lower bounds on the ratio of the diffusion coefficient to the squared average value in terms of suitable universal rates, independent of the empirical functional. These bounds are called "generalized thermodynamic uncertainty relations" (GTUR's), being generalized versions of the thermodynamic uncertainty relation to the time-periodic case and to functionals which are more general than currents. Previously, GTUR's in the time-periodic case have been obtained in [1,27,42]. Here we recover the GTUR's in [1,27] and produce new ones, leading to even stronger bounds and also to new trade-off relations for time-homogeneous systems. Moreover, we generalize to arbitrary protocols the GTUR obtained in [42] for time-symmetric protocols. We also generalize to the time-periodic case the GTUR obtained in [19] for the so called dynamical activity, and provide a new GTUR which, in the time-homogeneous case, is stronger than the one in [19]. The unifying picture is completed with a comprehensive comparison between the different GTUR's.

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Affinity- and topology-dependent bound on current fluctuations

Cited by 44 publications

References 22 publications

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Bounds on current fluctuations in periodically driven systems

A unifying picture of generalized thermodynamic uncertainty relations

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