The role of quantum information in thermodynamics—a topical review

Abstract

This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world. CONTENTS

Chemical Reactions Using a Non-Equilibrium Wigner Function Approach

“…Our MFPT studies are compared also briefly to other MFPT studies by other authors [35]. For the sake of a simpler presentation without loss of generality, the various approximations leading to the Smoluchowski-like equation for W [0] have been carried out in detail for a one-dimensional case in Appendices C-F. We point out that no use of non-equilibrium Wigner functions, moments and hierarchies was made in the works [22][23][24][25][26][27][28][29]. Among several open problems (and hence, possible future uses of the methods in the present paper), we quote: (a2) extensions to include more than one bound state between the two particles, thereby allowing for transitions among those states (eventually, for instance, transitions resembling vibrational ones approximately) and (b2) generalizations to more general two-particle chemical reactions (like A + B → C + D).…”

“…Section 2 deals with the non-equilibrium evolution of two quantum particles in three spatial dimensions, subject to an attractive potential between them and in contact with a large HB at thermal equilibrium. Throughout our study, we assume that the state of the system, for sufficiently long times, approaches towards its own canonical density operator at thermal equilibrium with the HB, in agreement with the results in [22][23][24][25][26][27][28][29]. We shall simplify the treatment by omitting the detailed analysis of the states of the HB (just retaining the fact that it establishes the temperature), and in an effective way, we will focus exclusively on the quantum states of the two particles.…”

“…The complicated structure of the hierarchy (C10) is a genuine consequence of quantum mechanics. By invoking [22][23][24][25][26][27][28][29], (C10) should simplify necessarily for very long t, with W n → 0 for n > 0, while W 0 = 0 with W 0 → W eq,0 and M 1,0 W eq,0 = 0. One expects that, for adequate t and by solving the hierarchy (C10) for n > 0, all W n for n > 0 can be expressed, through suitable linear operators, in terms of W 0 and of suitable initial conditions W in,n , for n > 0.…”

“…One first reason is that the research in [22][23][24][25][26][27][28][29] yielded an approach to the equilibrium canonical quantum distribution, independently both on the HB and, essentially, also on the initial state. Therefore, our starting point has been independent of the interactions and mechanisms determined by external sources (except on temperature, imposed by the HB).…”

“…In the quantum case: (a) even if, in general, Wigner functions could be negative in some domain [36,37], we shall argue that the actual equilibrium Wigner function could still be used as a weight function to generate orthogonal polynomials, by invoking a suitable mathematical framework (Section 2.4); (b) upon constructing the orthogonal polynomials, one integrates over the relative momentum q (while in [34], one integrated over all positions [z] of the atoms along the two chains); (c) even if the system approaches thermal equilibrium for sufficiently long times [22][23][24][25][26][27][28][29], the nonequilibrium evolution equation for the Wigner function (our starting point in Section 2) does not display either irreversibility or a thermalizing evolution in general (while the Kramers-like master equation in [34] did display them from the outset). Then, approximations (for short thermal wavelengths and long times) are necessary here in order to arrive at the actual irreversible Smoluchowski-like equation for the lowest non-equilibrium moment in Section 3.3.…”