Palestrante: Prof. Dr. Mário José de Oliveira (IFUSP)

Resumo:

Ordinary stochastic phenomena are well described by the Fokker-Planck- Kramers (FPK) equation which accounts for the classical dissipative behavior in a thermal environment. Quantum dissipation, on the other hand, cannot be explained by the classical FPK equation and requires an extension of the stochastic theory to the domain of quantum mechanics. The extension that we consider here is based on a quantum version of the classical FPK equation, which is obtained by the canonical quantization of the classical FPK equation. The dissipation and fluctuation terms are chosen as to ensure that in equilibrium the system is described by the Gibbs state. An expression for the quantum entropy production is also provided which properly describes quantum systems in a nonequilibrium stationary state. We also consider the quantum FPK equation for a system with many degrees of freedom, which is appropriate to describe a thermodynamic system in contact with one or several thermal reservoirs, which serves as the basis for a quantum thermodynamics or more properly a quantum stochastic mechanics. To this end it is necessary to define the rate of entropy production for quantum system which is also provided here. The approach is applied to several situations including a system of coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which the entropy production rate and the quantum thermal conductance are obtained.