Thermalization in Open Many-Body Systems and KMS Detailed Balance

2025/05/26 by Matteo Scandi, Álvaro M. Alhambra, Scandi, Matteo +2 · 2 voices · 13 citations
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Advanced Thermodynamics and Statistical Mechanics #Convergence (economics) #Detailed balance #Harmonic oscillator #Jump #Limit (mathematics) #Master equation #Material Dynamics and Properties #Quantum #Quantum many-body systems #Quantum master equation #Quantum system #Renormalization #Theoretical and Computational Physics #Thermal properties of materials #Thermalisation

paper · pdf · open access · doi:10.1103/sfp3-3sqf

published in Physical Review X 16(1) (American Physical Society)

openalex created_date 2025/12/22 · openalex publication_date 2025/12/22 · openalex updated_date 2026/03/01

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.

Citations

• Simulation methods for open quantum many-body systems
• The χ ²χ2-divergence and mixing times of quantum Markov processes
• Completely positive dynamical semigroups of N-level systems
• Completely positive linear maps on complex matrices
• Rapid Quantum Ground State Preparation via Dissipative Dynamics

Cited by

• Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion
• The Trinity of Markovian Quantum Thermodynamics: Unifying the Axiomatic, Microscopic, and Operational Paradigms
• Is Lindblad for me?
• End-to-End Efficient Quantum Thermal and Ground State Preparation Made Simple
• Rapid Quantum Ground State Preparation via Dissipative Dynamics
• Beyond Lindblad Dynamics: Rigorous Guarantees for Thermal and Ground State Preservation under System Bath Interactions
• Initial-State Typicality in Quantum Relaxation
• Exact and approximate conditions of tabletop reversibility: when is Petz recovery cost-free?
• Fast Mixing of Quantum Spin Chains at All Temperatures
• Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra
• Numerical implementation of the partial secular approximation and unified master equation in structured open quantum systems
• Thermalization with partial information
• Davies equation without the secular approximation: Reconciling locality with quantum thermodynamics for open quadratic systems
• Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage
• Restoring the second law to classical-quantum dynamics

Discussions

• New paper today! Very excited to announce we obtain, from first principles, a quantum master equation that both applies in the many-body regime and provably converges to the exact Gibbs state: arxiv.o [bsky, 21 points, 1 comments]
• (6/14) Bergamaschi & Chen show that any 1D spin chain with nearest-neighbour int. can thermalise at any temperature, using clustering of correlations methods. This is a step forward, relaxing earlier [bsky, 2 points, 1 comments]

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