Exploring Planckian Thermalization Time in Strongly Coupled Open Quantum Systems

Abstract

Thermalization times in open quantum systems are often constrained using quantum speed limits formulated for a fixed Hamiltonian or a prescribed dynamical trajectory. Such bounds can become trivial at strong system–environment coupling and do not directly capture thermalization as a robust process that must adapt to different system Hamiltonians. In this thesis, we study an alternative information-theoretic approach based on the distinguishability of equilibrium states associated with a family of nearby Hamiltonians. Within this framework, thermalization is viewed as a Hamiltonian-estimation task, leading to Planckian lower bounds on thermalization times that depend only on equilibrium-state sensitivity and not on the microscopic relaxation path. We extend this formulation to strongly coupled open quantum systems, where the relevant equilibrium state is the mean-force Gibbs state rather than the Gibbs state of the bare Hamiltonian. We investigate the resulting bounds in exactly solvable fermionic models and in spin–boson models across different coupling regimes. We show that strong coupling does not generically remove Planckian constraints: when the reduced equilibrium state retains information about the system Hamiltonian, nontrivial lower bounds on thermalization times persist.