Nonequilibrium-thermodynamics approach to open quantum systems

Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local-in-time master equation that provides a direct connection for dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated by the application to the damped harmonic oscillator and the damped driven two-level system, resulting in analytical expressions for the non-Markovian and nonequilibrium entropy and inverse temperature.

Figure 1

(top) Entropy and (bottom) inverse temperature for the damped oscillator. Parameters in the system are $W=10,{\beta }_{\text{bath}}=3.$

Figure 2

(top) Entropy and (bottom) inverse temperature for the driven two-level system. Parameters in the system are $W=10,{\beta }_{\text{bath}}=3,\Omega =5.$