Strong-coupling quantum thermodynamics of quantum Brownian motion based on the exact solution of its reduced density matrix

The strong system-reservoir coupling prevents the thermal equilibrium state of systems from being expressed as a Gibbs state with bare system Hamiltonian. Correspondingly, many thermodynamic quantities must be redefined. In particular, for the heat capacity of strongly coupled quantum Brownian motion, there has been controversy regarding inconsistencies in different definitions and the anomalous negative heat capacity. Here, the authors rigorously solve the reduced density matrix of quantum Brownian motion and obtain the renormalized Hamiltonian and reduced partition function. This resolves the controversy about the heat capacity under strong coupling.