Quantum decoherence and thermalization at finite temperature within the canonical-thermal-state ensemble

We study measures of decoherence and thermalization of a quantum system S in the presence of a quantum environment (bath) E. The entirety S E is prepared in a canonical-thermal state at a finite temperature; that is, the entirety is in a steady state. Both our numerical results and theoretical predictions show that measures of the decoherence and the thermalization of S are generally finite, even in the thermodynamic limit, when the entirety S E is at finite temperature. Notably, applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider S uncoupled from E, but entangled with E, to predict decoherence and thermalization measures of S. This decoupling allows closed-form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of S and of E. Large-scale numerical results for both coupled and uncoupled entireties with up to 40 quantum spins support these findings.