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This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of…

Statistical Mechanics · Physics 2016-08-02 Luca D'Alessio , Yariv Kafri , Anatoli Polkovnikov , Marcos Rigol

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of…

Statistical Mechanics · Physics 2026-01-14 Maksym Serbyn , Alexander Avdoshkin , Oriana K. Diessel , David A. Huse

Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation…

Statistical Mechanics · Physics 2025-04-11 Bruno Bertini , Katja Klobas , Pavel Kos , Daniel Malz

Deriving conditions under which a macroscopic system thermalizes directly from the underlying quantum many-body dynamics of its microscopic constituents is a long-standing challenge in theoretical physics. The well-known eigenstate…

Statistical Mechanics · Physics 2022-02-02 Lennart Dabelow , Patrick Vorndamme , Peter Reimann

Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. In…

Statistical Mechanics · Physics 2026-03-25 Lennart Dabelow , Christian Eidecker-Dunkel , Peter Reimann

We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…

Quantum Physics · Physics 2021-03-08 Ashkan Shekaari , Mahmoud Jafari

A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…

Quantum Physics · Physics 2013-05-08 J. M. Deutsch , Haibin Li , Auditya Sharma

Emulating thermal observables on a digital quantum computer is essential for quantum simulation of many-body physics. However, thermalization typically requires a large system size due to incorporating a thermal bath, whilst limited…

Quantum Physics · Physics 2025-03-12 H. Perrin , T. Scoquart , A. I. Pavlov , N. V. Gnezdilov

We investigate dynamical equilibration of expectation values in closed quantum systems for realistic non-equilibrium initial states. Thereby we find that the corresponding long time expectation values depend on the initial expectation…

Statistical Mechanics · Physics 2017-06-28 Christian Bartsch , Jochen Gemmer

Two identical finite quantum systems prepared initially at different temperatures, isolated from the environment, and subsequently brought into contact are demonstrated to relax towards Gibbs-like quasi-equilibrium states with a common…

Statistical Mechanics · Physics 2011-01-10 Alexey V. Ponomarev , Sergey Denisov , Peter Hänggi

Advances in controlling and measuring systems of ultra-cold atoms provided strong motivation to theoretical investigations of quantum dynamics in closed many-body systems. Fundamental questions on quantum dynamics and statistical mechanics…

Quantum Gases · Physics 2015-12-04 Ehud Altman

Quantum thermalization in a many-body system is defined by the approach of local subsystems towards a universal form, describable as an ensemble of quantum states wherein observables acquire thermal expectation values. Recently, it was…

Quantum Physics · Physics 2023-09-19 Matteo Ippoliti , Wen Wei Ho

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…

Quantum Physics · Physics 2023-06-07 Neil Dowling , Pedro Figueroa-Romero , Felix A. Pollock , Philipp Strasberg , Kavan Modi

Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is…

Quantum Physics · Physics 2020-01-08 A. H. Skelt , K. Zawadzki , I. D'Amico

In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to…

Statistical Mechanics · Physics 2023-11-30 Aram W. Harrow , Yichen Huang

In quantum statistical mechanics, closed many-body systems that do not exhibit thermalization after an arbitrarily long time in spite of the presence of interactions are called as many-body localized systems, and recently have been…

High Energy Physics - Theory · Physics 2018-12-14 Fumihiko Sugino , Pramod Padmanabhan

The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 S. Camalet

We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to…

Quantum Physics · Physics 2012-11-27 A. Smirne , E. -M. Laine , H. -P. Breuer , J. Piilo , B. Vacchini

The irreversibility and thermalization of many-body systems can be attributed to the erasure of spread non-equilibrium state information by local operations. This thermalization mechanism can be demonstrated by the sequence of…

Quantum Physics · Physics 2025-11-24 Xue-Yi Guo

When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where…

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