Stiffness of probability distributions of work and Jarzynski relation for non-Gibbsian initial states

Schmidtke, Daniel; Knipschild, Lars; Campisi, Michele; Steinigeweg, Robin; Gemmer, Jochen

doi:10.1103/physreve.98.012123

Cited by 20 publications

(16 citation statements)

References 64 publications

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“…[49] theoretically showed the second law at the average level in the long-time regime on the basis of the ETH. Also in previous papers [50,51], it has been numerically suggested that the fluctuation theorem holds even in the long-time regime. Given these researches, it is desirable to make a comprehensive understanding of the validity of the fluctuation theorem in the entire time domain.…”

Section: Introductionmentioning

confidence: 91%

Eigenstate Fluctuation Theorem in the Short and Long Time Regimes

Iyoda,

Kaneko,

Sagawa

2021

Preprint

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The canonical ensemble plays a crucial role in statistical mechanics in and out of equilibrium. For example, the standard derivation of the fluctuation theorem relies on the assumption that the initial state of the heat bath is the canonical ensemble. On the other hand, the recent progress in the foundation of statistical mechanics has revealed that a thermal equilibrium state is not necessarily described by the canonical ensemble but can be a quantum pure state or even a single energy eigenstate, as formulated by the eigenstate thermalization hypothesis (ETH). Then, a question raised is how these two pictures, the canonical ensemble and a single energy eigenstate as a thermal equilibrium state, are compatible in the fluctuation theorem. In this paper, we theoretically and numerically show that the fluctuation theorem holds in both of the long and short-time regimes, even when the initial state of the bath is a single energy eigenstate of a many-body system. Our proof of the fluctuation theorem in the long-time regime is based on the ETH, while it was previously shown in the short-time regime on the basis of the Lieb-Robinson bound and the ETH [Phys. Rev. Lett. 119, 100601 (2017)]. The proofs for these time regimes are theoretically independent and complementary, implying the fluctuation theorem in the entire time domain. We also perform a systematic numerical simulation of hard-core bosons by exact diagonalization and verify the fluctuation theorem in both of the time regimes by focusing on the finite-size scaling. Our results contribute to the understanding of the mechanism that the fluctuation theorem emerges from unitary dynamics of quantum many-body systems, and can be tested by experiments with, e.g., ultracold atoms.

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Section: Introductionmentioning

confidence: 91%

Eigenstate Fluctuation Theorem in the Short and Long Time Regimes

Iyoda,

Kaneko,

Sagawa

2021

Preprint

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“…Quantum phase transitions (QPTs) are an exquisitely quantum phenomenon, so there is interest in studying their signatures on quantum thermodynamic quantities and their distributions (fluctuations) [14,16,18,[21][22][23][24][25][26][27][28]. In addition, many-body interactions, which are ubiquitous and notoriously difficult to treat, assume an even more complex role in out-of-equilibrium quantum systems [29,30] where, e.g., they may affect the way the system reaches or settles into different phases.…”

mentioning

confidence: 99%

Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

Zawadzki

Serra

D’Amico

2020

Phys. Rev. Research

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The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of the system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a nonequilibrium dynamics. By driving transient currents to oppose the precursor to the metal-Mott-insulator transition in a diversity of dynamical regimes, we show how increasing many-body interactions dramatically affect the statistics of energy fluctuations and, consequently, the extractable work distribution of finite Hubbard chains. Statistical properties of such distributions as its skewness with its impressive change across the transition can be related to irreversibility and entropy production. Even for slow driving rates, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong features in the work distribution. In the Mott-insulating phase, the work fluctuation-dissipation balance gets modified with the irreversible entropy production dominating over work fluctuations. Because of this, effects of an interaction-driven quantum phase transition on thermodynamic quantities and irreversibility must be considered in the design of protocols in small-scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols on a quantum scale.

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“…Just as for the second law, the underlying mechanisms which render these theorems valid or invalid are still under discussion. In this work, we will show that the validity of the IFT for microcanonical and pure quantum states follows from natural assumptions on transition probabilities we call "stiffness" and "smoothness" [1,2]. In essence, stiffness states that transition probabilities are largely independent of the initial energies.…”

Section: Introductionmentioning

confidence: 93%

Integral Fluctuation Theorem for Microcanonical and Pure States

Heveling,

Wang,

Gemmer

2021

Preprint

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We present a derivation of the integral fluctuation theorem (IFT) for isolated quantum systems based on some natural assumptions on transition probabilities. Under these assumptions of "stiffness" and "smoothness" the IFT immediately follows for microcanonical and pure quantum states. We numerically check the IFT as well as the validity of our assumptions by analyzing two exemplary systems. We have been informed by T. Sagawa et al. that he and his co-workers found comparable numerical results and are preparing a corresponding paper, which should be available on the same day as the present text. We recommend reading their submission.

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Stiffness of probability distributions of work and Jarzynski relation for non-Gibbsian initial states

Cited by 20 publications

References 64 publications

Eigenstate Fluctuation Theorem in the Short and Long Time Regimes

Eigenstate Fluctuation Theorem in the Short and Long Time Regimes

Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

Integral Fluctuation Theorem for Microcanonical and Pure States

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