Fluctuating Work: From Quantum Thermodynamical Identities to a Second Law Equality

Abstract

We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics. By including a work system whose energy is allowed to fluctuate, we derive a set of equalities which all thermodynamical transitions have to satisfy. This extends the condition for maps to be Gibbs-preserving to the case of fluctuating work, providing a more general characterisation of maps commonly used in the information theoretic approach to thermodynamics. For final states, block diagonal in the energy basis, this set of equalities are necessary and sufficient conditions for a thermodynamical state transition to be possible. The conditions serves as a parent equation which can be used to derive a number of results. These include writing the second law of thermodynamics as an equality featuring a fine-grained notion of the free energy. It also yields a generalisation of the Jarzynski fluctuation theorem which holds for arbitrary initial states, and under the most general manipulations allowed by the laws of quantum mechanics. Furthermore, we show that each of these relations can be seen as the quasi-classical limit of three fully quantum identities. This allows us to consider the free energy as an operator, and allows one to obtain more general and fully quantum fluctuation relations from the information theoretic approach to quantum thermodynamics.

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

“…Describing work fluctuations in genuinely coherent processes remains a subtle and open question in quantum thermodynamics, although relevant progress has been achieved recently [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][38][39][40]. Here we report the first experimental observation of work distributions, or, more precisely of transition probabilities, using an implementation based on a CM scheme [18].…”

A quantum Szilard engine without heat from a thermal reservoir

“…In recent years, much attention has been paid to the interplay between quantum theory and thermodynamics [13][14][15][16][17][18][19][20][21][22][23]. This has included the extension of work extraction through feedback control to the quantum regime, culminating in both theoretical [24][25][26][27][28][29] and experimental [30,31] investigations.…”

Work extraction from quantum systems with bounded fluctuations in work

“…However, for general state transformations (which we do not analyse in this paper) the presence of coherences in the initial and final states of system generate further constraints on the work1213. Regarding quantum definitions of work, several attempts have been made141516, but there is still no consensus on these definitions and their treatment of fluctuations. The problem of defining a truly quantum definition of work, or if such a definition exists, remains an important and open question161718.…”