Thermodynamic Processes Generated by a Class of Completely Positive Quantum Operations

Abstract

An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as the von Neumann entropy monotonically increases under the operations. The fixed point analysis shows that repeated applications of these operations to a given system transform from its pure ground state at zero temperature to the completely random state in the high temperature limit with intermediate states being generically out of equilibrium. It is shown that the Clausius inequality can be violated along the processes, in general. A bipartite spin-1/2 system is analyzed as an explicit example.

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

“…Closing this section, we wish to correct a statement made in Ref. [4]. Unlike what is claimed there, the above results manifestly show that the operators in Eq.…”

“…In other words, the objective system undergoes a sequence of "discrete measurements" by the environment as an "observer". It has been indicated [4] that the Clausius inequality could be violated along such a process, exhibiting a remarkable quantum effect on thermodynamics. Now, given a pure state at vanishing temperature, mapping from it to a target mixed state is not unique.…”

Corrigendum to “Completely-positive quantum operations generating thermostatistical states: A comparative study” [Physica A 409 (2014) 130–137]

“…We shall see that the entropy exhibits a nonmonotonic behavior and may even decrease under repeated applications of the operation associated with thermofield dynamics, in contrast to monotonic increase in the wide sense under the one in Refs. [4][5][6]. The result can be interpreted in terms of the concept of unitalness.…”

“…This idea forms a core of a recent work in Ref. [4]. There, an effect of the (hot) heat bath is represented by a heat-up operation given in terms of a completely-positive map proposed in Refs.…”

“…It has been indicated [4] that the Clausius inequality could be violated along such a process, exhibiting a remarkable quantum effect on thermodynamics. Now, given a pure state at vanishing temperature, mapping from it to a target mixed state is not unique.…”