Multimode Brownian oscillators: Thermodynamics and heat transport

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach directly gives the exact time-local equation of motion for reduced density operator, from which we can easily extract both the reduced system and hybrid bath dynamical informations. Two representative entangled system-bath quantities, the heat transport and the thermodynamics of quantum mixing, are studied. The heat current is obtained from both the algebraic method and the discrete imaginary-frequency method followed by the Meir-Wingreen's formula. It is anticipated that the algebraic method developed in this work would constitute a crucial component for nonequilibrium statistical mechanics for open quantum systems.