Unified thermodynamic-kinetic uncertainty relation

Vo, Van Tuan; Vu, Tan Van; Hasegawa, Yoshihiko

doi:10.48550/arxiv.2203.11501

Cited by 3 publications

(6 citation statements)

References 41 publications

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“…Note that we derived the classical speed limit and thermodynamic uncertainty relation in a unified way in Refs. [27,65]. However, Refs.…”

Section: Geometric Bound In Probability Spacementioning

confidence: 99%

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Thermodynamic bounds via bulk-boundary correspondence: speed limit, thermodynamic uncertainty relation, and Heisenberg principle

Hasegawa¹

2022

Preprint

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Strongly correlated and coupled systems are difficult to analyze, because of inability to apply perturtative approaches. The bulk-boundary correspondence gives a guiding principle for tackling such systems, which states that all information of the bulk of a system is encoded in its boundary. In this paper, we apply the concept of the bulk-boundary correspondence to thermodynamic bounds described by classical and quantum Markov processes. Using the continuous matrix product state, we can convert a Markov process to a quantum field, which correspond to the boundary and the bulk, respectively, and jump events in the Markov process are represented by particle creation in the bulk quantum field. Introducing the time evolution of the bulk quantum field, we apply the notion of the geometric bound to the time evolution. We find that the geometric bound reduces to the speed limit relation when we represent the bound in terms of boundary quantities, whereas it reduces to the thermodynamic uncertainty relation when the bound is expressed by quantities of the bulk quantum field. Our results show that the speed limit and the thermodynamic uncertainty relations can be derived from the same ancestral inequality, showing that they are two faces of the same geometric bound. Moreover, we show that the Heisenberg uncertainty relation in the bulk quantum field reduces to the thermodynamic uncertainty relation in the Markov process.

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“…Note that we derived the classical speed limit and thermodynamic uncertainty relation in a unified way in Refs. [27,65]. However, Refs.…”

Section: Geometric Bound In Probability Spacementioning

confidence: 99%

“…However, Refs. [27,65] derived the classical speed limit as a short time limit of the thermodynamic uncertainty relation, while the derivation here does not use the short time limit. Therefore, our approach is purely based on the common ancestral relation.…”

Section: Geometric Bound In Probability Spacementioning

confidence: 99%

Thermodynamic bounds via bulk-boundary correspondence: speed limit, thermodynamic uncertainty relation, and Heisenberg principle

Hasegawa¹

2022

Preprint

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“…We basically follow the notation of Ref. [13]. We consider a discrete-state system described by a continuous-time Markov jump process.…”

Section: Preliminariesmentioning

confidence: 99%

“…is the probability current from state m to state n. The pseudo-entropy production satisfies the following inequality (see Ref. [13]).…”

Section: Preliminariesmentioning

confidence: 99%

“…On the other hand, the kinetic uncertainty relation (KUR) imposes an another upper bound on generic observables by the dynamical activity [3]. Recently, for discrete-state systems modeled by continuous-time Markov jump processes, a unified bound of the thermodynamic and kinetic uncertainty relation (hereinafter referred to as the TKUR) has been derived [13]. This bound is always tighter than the TUR and KUR, and the bound is written as the product of the dynamical activity and function of the ratio of entropy production to dynamical activity.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic-kinetic uncertainty relation: properties and an information-theoretic interpretation

Nishiyama¹

2022

Preprint

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Universal relations that characterize the fluctuations of nonequilibrium systems are of fundamental importance. The thermodynamic and kinetic uncertainty relations impose upper bounds on the precision of currents solely by total entropy production and dynamical activity, respectively. Recently, a tighter bound that imposes on the precision of currents by both total entropy production and dynamical activity has been derived (referred to as the TKUR). In this paper, we show that the TKUR gives the tightest bound of a class of inequalities that imposes an upper bound on the precision of currents by arbitrary functions of the entropy production, dynamical activity, and time interval. Furthermore, we show that the TKUR can be rewritten as an inequality between two Kullback-Leibler divergences. One comes from the ratio of entropy production to dynamical activity, the other comes from the Kullback-Leibler divergence between two probability distributions defined on two-element set, which are characterized by the ratio of precision of the time-integrated current to dynamical activity.

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Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining

Ghosal

Bisker

2022

Phys. Chem. Chem. Phys.

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Unified thermodynamic-kinetic uncertainty relation

Cited by 3 publications

References 41 publications

Thermodynamic bounds via bulk-boundary correspondence: speed limit, thermodynamic uncertainty relation, and Heisenberg principle

Thermodynamic bounds via bulk-boundary correspondence: speed limit, thermodynamic uncertainty relation, and Heisenberg principle

Thermodynamic-kinetic uncertainty relation: properties and an information-theoretic interpretation

Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining

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