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Thermalization in Open Many-Body Systems and KMS Detailed Balance

Matteo Scandi ^* and Álvaro M. Alhambra ^†

Instituto de Física Téorica UAM/CSIC, C. Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain

^*Contact author: matteo.scandi@csic.es
^†Contact author: alvaro.alhambra@csic.es

Phys. Rev. X 16, 011040 – Published 27 February, 2026

DOI: https://doi.org/10.1103/sfp3-3sqf

Abstract

Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems, with Hamiltonians with vanishingly small energy spacings that forbid that approximation. The equation satisfies a general form of detailed balance, called KMS (Kubo-Martin-Schwinger), which ensures exact convergence to the many-body Gibbs state. Unlike the more common notion of GNS (Gelfand-Naimark-Segal) detailed balance, this notion is compatible with the absence of the rotating wave approximation. We show that the resulting Lindbladian dynamics not only reproduces the thermal equilibrium point up to a small renormalization of the system Hamiltonian, but it also approximates the true system evolution with an error that grows at most linearly in time, giving an exponential improvement upon previous estimates. This master equation has quasilocal jump operators, can be efficiently simulated on a quantum computer, and reduces to the usual Davies dynamics in the limit of a coarse-graining time much larger than the inverse of the smallest frequency difference. With it, we provide a rigorous model of many-body thermalization relevant to both open quantum systems and quantum algorithms.

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Understanding how quantum systems reach thermal equilibrium from microscopic principles is a central challenge in statistical mechanics. We derived a universal quantum master equation from first principles that describes the weak interaction between a generic many-body system and a thermal bath without relying on the restrictive rotating wave approximation. This approach utilizes Kubo-Martin-Schwinger detailed balance, a general symmetry principle that ensures the system converges to the correct many-body Gibbs state even when energy levels are densely packed. Our resulting model approximates true system evolution with an error that grows only linearly in time, representing an exponential improvement over previous estimates. Because the equation uses quasilocal operators, it can be efficiently simulated on quantum computers to mimic complex thermalization processes. This work provides a rigorous framework for studying open many-body dynamics and developing advanced quantum algorithms for Gibbs sampling.

Article Text

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Phys. Rev. X 16, 011040– Published 27 February, 2026

Vol. 16, Iss. 1 — January - March 2026

Received 5 June 2025
Revised 13 November 2025
Accepted 22 December 2025

DOI: https://doi.org/10.1103/sfp3-3sqf

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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Thermalization in Open Many-Body Systems and KMS Detailed Balance

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