  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.
