Quantum nonequilibrium equalities with absolute irreversibility

Abstract

We derive quantum nonequilibrium equalities in absolutely irreversible processes. Here by absolute irreversibility we mean that in the backward process the density matrix does not return to the subspace spanned by those eigenvectors that have nonzero weight in the initial density matrix. Since the initial state of a memory and the postmeasurement state of the system are usually restricted to a subspace, absolute irreversibility occurs during the measurement and feedback processes. An additional entropy produced in absolutely irreversible processes needs to be taken into account to derive nonequilibrium equalities. We discuss a model of a feedback control on a qubit system to illustrate the obtained equalities. By introducing N heat baths each composed of a qubit and letting them interact with the system, we show how the entropy reduction via feedback control can be converted into work. An explicit form of extractable work in the presence of absolute irreversibility is given.

Quantum-trajectory thermodynamics with discrete feedback control

“…In the presence of feedback control, by adding certain correction terms due to measurement [15][16][17], we can derive some generalized fluctuation theorems.…”

“…Derivation of the relevant information gain (17) To derive the second generalized Jarzynski equality, we again make use of Eq. (D4).…”

“…The main difficulty is to identify the thermodynamic variables and the information content compatible with genuine quantum effects such as superposition and measurement backaction. The thermodynamics of information processing has been discussed mainly on the basis of statistical ensembles [10][11][12][13][14], whereas only special cases have been examined at the trajectory level including classical measurement errors [15], an isolated driving [16] and a separated thermalization process [17].…”

Optimal work of the quantum Szilard engine under isothermal processes with inevitable irreversibility

“…To optimize the work of a classical multi-particle SZE, Horowitz and Parrondo have proposed an extremely sophisticated protocol to make the feedback process reversible [14]. On the other hand, achievable bounds of extractable work [15], non-equilibrium equalities [16], and its quantum version [17] have been found with the irreversibility kept intact. Recently Wehner et al report the relation between the reversibility of quantum thermodynamic processes and the corresponding work [18].…”

“…The main question addressed in this paper is what the optimal condition of extractable work of the quantum SZE is when its inevitable irreversibility [13,[15][16][17]21] is taken into account. Due to the irreversibility an initial state at the stage that the inevitably irreversible process occurs cannot be automatically restored when the timebackward process is performed.…”