An information-theoretic proof of the Planckian bound for thermalization

• URL: http://arxiv.org/abs/2506.19188v1
• Date: Mon, 23 Jun 2025 23:25:01 GMT
• Title: An information-theoretic proof of the Planckian bound for thermalization
• Authors: Paolo Abiuso, Alberto Rolandi, John Calsamiglia, Pavel Sekatski, Martí Perarnau-Llobet,
• Abstract summary: We show that quantum mechanics entails a fundamental lower bound on the thermalization time $tau$ of any system.<n>In the low-temperature regime, our bound takes the form $tau geq hbar / Delta$ with $Delta$ the spectral gap.<n>These bounds, rooted in Hamiltonian estimation, hold for arbitrary quantum processes that output states close to the corresponding thermal ensemble for a nontrivial class of Hamiltonians.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We demonstrate that quantum mechanics entails a fundamental lower bound on the thermalization time $\tau$ of any system. At finite temperature, we show that $\tau$ is bounded by half the Planckian dissipation time, $\tau \geq \tau_{\rm Pl}/2$ with $\tau_{\rm Pl} = \hbar/(k_{\rm B} T)$. In the low-temperature regime, our bound takes the form $\tau \geq \hbar / \Delta$ with $\Delta$ the spectral gap, in close connection with the quantum adiabatic theorem. These bounds, rooted in Hamiltonian estimation, hold for arbitrary quantum processes that output states close to the corresponding thermal ensemble for a nontrivial class of Hamiltonians.

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