Operationally Accessible Bounds on Fluctuations and Entropy Production in Periodically Driven Systems

Koyuk, Timur; Seifert, Udo

doi:10.1103/physrevlett.122.230601

Cited by 104 publications

(87 citation statements)

References 68 publications

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“…σ is bounded from below by j 2 /D. The TUR has been proven for a Markovian dynamics on a general network by Gingrich et al [2,3] and further investigated for a number of different settings, both in the classical (see, e.g., [4][5][6][7][8][9][10][11][12][13][14][15]) and the quantum domain (see, e.g., [16][17][18][19][20][21][22]).…”

Section: Introductionmentioning

confidence: 99%

Field-Theoretic Thermodynamic Uncertainty Relation

2020

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We propose a field-theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a Markovian dynamics on a discrete set of states and for overdamped Langevin equations. We first formulate a framework which describes quantities like current, entropy production and diffusivity in the case of a generic field theory. We will then apply this general setting to the one-dimensional Kardar-Parisi-Zhang equation, a paradigmatic example of a non-linear field-theoretic Langevin equation. In particular, we will treat the dimensionless Kardar-Parisi-Zhang equation with an effective coupling parameter measuring the strength of the non-linearity. It will be shown that a field-theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant. The calculations show that the field-theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the Kardar-Parisi-Zhang equation due to an excess term stemming from its non-linearity.

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Section: Introductionmentioning

confidence: 99%

Field-Theoretic Thermodynamic Uncertainty Relation

2020

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“…Equation (7) tells us that efficiency close to the Carnot value and high power entail large fluctuations. We note that the bound (8) has recently been generalized to periodically driven systems [93].…”

Section: Coupled Transportmentioning

confidence: 99%

Anomalous Heat Transport in Classical Many-Body Systems: Overview and Perspectives

2020

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In this review paper we survey recent achievements in anomalous heat diffusion, while highlighting open problems and research perspectives. First, we briefly recall the main features of the phenomenon in low-dimensional classical anharmonic chains and outline some recent developments in the study of perturbed integrable systems and the effect of long-range forces and magnetic fields. Selected applications to heat transfer in material science at the nanoscale are described. In the second part, we discuss of the role of anomalous conduction in coupled transport and describe how systems with anomalous (thermal) diffusion allow a much better power-efficiency trade-off for the conversion of thermal to particle current.

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“…Subsequently, the violation of the original bound has been found for other dynamics, e.g., for discrete-time Markov chains [9], transport systems [10], and underdamped dynamics [11,12]. TURs have been intensively refined in other contexts that include both classical and quantum systems [12][13][14][15][16][17][18][19][20][21][22][23]. A remarkable application of TURs is the estimation of entropy production [24].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic uncertainty relations under arbitrary control protocols

Hasegawa

2020

Phys. Rev. Research

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Thermodynamic uncertainty relations quantifying a trade-off between current fluctuation and entropy production have been found in various stochastic systems. Herein, we study the thermodynamic uncertainty relations for Langevin systems driven by an external control protocol. Using information-theoretic techniques, we derive the uncertainty relations for arbitrary observables satisfying a scaling condition in both overdamped and underdamped regimes. We prove that the observable fluctuation is constrained by both entropy production and a kinetic term. The derived bounds are applicable to both current and noncurrent observables, and hold for arbitrary time-dependent protocols, thus providing a wide range of applicability. We illustrate our universal bounds with the help of three systems: a dragged Brownian particle, a Brownian gyrator, and a stochastic underdamped heat engine.

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Operationally Accessible Bounds on Fluctuations and Entropy Production in Periodically Driven Systems

Cited by 104 publications

References 68 publications

Field-Theoretic Thermodynamic Uncertainty Relation

Field-Theoretic Thermodynamic Uncertainty Relation

Anomalous Heat Transport in Classical Many-Body Systems: Overview and Perspectives

Thermodynamic uncertainty relations under arbitrary control protocols

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