Completely-positive quantum operations generating thermostatistical states: A comparative study

Nonunitary quantum operations generating thermostatistical states and forming positive operator-valued measures (POVMs) are of current interest as a useful tool for operational approach to quantum thermodynamics. Here, two different operations generating the same thermostatistical state are studied: one is related to thermofield dynamics and the other is the one proposed in a recent work [S. Abe, A. R. Usha Devi, A. K. Rajagopal, J. Phys. A: Math. Theor. 43 (2010) 045303]. A comparable study on them shows different behaviors of the von Neumann entropy under repeated applications of these two operations. It is shown that the entropy does not behave monotonically, in general, and can even decrease under the thermofield-dynamical one, in contrast to monotonic increase under the other.