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

Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions. Key examples are provided by the Crooks and Jarzynski relations: taking into account fluctuations in non-equilibrium dynamics, such relations connect equilibrium properties of thermodynamical relevance with explicit non-equilibrium features. Although the experimental verification of such fundamental relations in the classical domain has encountered some success, their quantum mechanical version requires the assessment of the statistics of work performed by or onto an evolving quantum system, a step that has so far encountered considerable difficulties in its implementation due to the practical difficulty to perform reliable projective measurements of instantaneous energy states. In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relationfollowing a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system. Our experimental approach has enabled the full characterisation of the out-of-equilibrium dynamics of a quantum spin in a statistically significant way, thus embodying a key step towards the grounding of quantum-systems thermodynamics.The verification and use of quantum fluctuation relations [1][2][3] requires the design of experimentally feasible strategies for the determination of the work distribution following a process undergone by a system. In the quantum regime, the concept of work done by or on a system needs to be reformulated [4] so as to include ab initio both the inherent non-deterministic nature of quantum dynamics and the effects of quantum fluctuations. In this sense, work acquires a meaning only as a statistical expectation value W = W P(W) dW that accounts for the possible trajectories followed by a quantum system across its evolution, as formalised by the associated work probability distribution P(W) = n,m p 0 n p τ m|n δ W − ( m − n ) . In order to understand this expression, let us consider a quantum system initially at equilibrium at temperature T and undergoing a quantum process that changes its Hamiltonian asĤ(0) →Ĥ(τ) within a time period τ. Then, p 0 n is the probability to find the system in the eigenstate |n(0) ofĤ(0) (with energy n ) at the start of the protocol, while p τ m|n = | m(τ)|Û|n(0) | 2 is the conditional probability to find it in the eigenstate |m(τ) ofĤ(τ) (with energy m ) if it was in |n(0) at t = 0 and evolved under the action of the propagatorÛ. P(W) encompasses the statistics of the initial state (given by p 0 n ) and the fluctuations arising from quantum measurement statistics (given by p τ m|n ). One can define a backward process that, starting from the equilibrium state of the system associated withĤ(τ) and temperature T , implements the protocolĤ(τ) →Ĥ(0) and thus inverting the control sequence of the ...

We propose an experimental scheme to verify the quantum nonequilibrium fluctuation relations using current technology. Specifically, we show that the characteristic function of the work distribution for a nonequilibrium quench of a general quantum system can be extracted by Ramsey interferometry of a single probe qubit. Our scheme paves the way for the full characterization of nonequilibrium processes in a variety of quantum systems, ranging from single particles to many-body atomic systems and spin chains. We demonstrate our idea using a time-dependent quench of the motional state of a trapped ion, where the internal pseudospin provides a convenient probe qubit.

Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.