An information-theoretic proof of the Planckian bound for thermalization

Abstract

It has been conjectured that the speed of thermalization is universally constrained by a Planckian timescale, τ Pl = ℏ /( k B T ), determined solely by the reduced Planck constant ℏ, Boltzmann’s constant ( k B ) and the temperature ( T ). However, a general and model-independent derivation of this limit has remained elusive. Here we provide a general proof of the emergence of Planckian thermalization based on quantum information geometry and quantum metrology. We formulate thermalization as a process that prepares states close to the corresponding thermal ensemble for a set of distinct Hamiltonians, and show that quantum mechanics imposes a universal lower bound τ  ≥  τ Pl /2 on the thermalization time τ at finite temperature. In the low-temperature regime, the spectral gap Δ between the ground and first excited states replaces the temperature as the relevant energy scale and determines the lower bound on the thermalization time, in close connection with the quantum adiabatic theorem. These bounds, rooted in Hamiltonian estimation, establish operational limits on thermalization governed exclusively by fundamental constants and the intrinsic energy scale.