An information-theoretic proof of the Planckian bound for thermalization

TL;DR

This paper provides an information-theoretic proof that quantum mechanics imposes a fundamental lower limit on thermalization time, linking it to the Planckian dissipation time and spectral gap, applicable to a broad class of quantum processes.

Contribution

It introduces a novel information-theoretic proof establishing a fundamental lower bound on thermalization time in quantum systems, connecting it to the Planckian bound and spectral gap.

Findings

Thermalization time is bounded below by half the Planckian dissipation time.

At low temperatures, the bound relates to the inverse spectral gap.

The bounds apply to general quantum processes producing thermal states.

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.