Work is an essential concept in classical thermodynamics, and in the quantum regime, where the notion of a trajectory is not available, its definition is not trivial. For driven (but otherwise isolated) quantum systems, work can be defined as a random variable, associated with the change in the internal energy. The probability for the different values of work captures essential information describing the behaviour of the system, both in and out of thermal equilibrium. In fact, the work probability distribution is at the core of “fluctuation theorems” in quantum thermodynamics. Here we present the design and implementation of a quantum work meter operating on an ensemble of cold atoms, which are controlled by an atom chip. Our device not only directly measures work but also directly samples its probability distribution. We demonstrate the operation of this new tool and use it to verify the validity of the quantum Jarzynksi identity.

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.

We study the decoherence process for an open quantum system that is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators). We carefully analyze the time dependence of the rate of entropy production showing that it has two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength); for longer times (but before equilibration) it is fixed by dynamical properties of the system (and is related to the Lyapunov exponent). The nature of the transition time between both regimes is investigated and the issue of quantum to classical correspondence is addressed. Finally, the impact of the interaction with the environment on coherent tunneling is analyzed.

We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency ${\omega }_d$ we show entanglement exists between environmental modes whose frequencies satisfy the condition ${\omega }_i+{\omega }_j={\omega }_d$. We show that this entanglement can persist for temperatures that can be significantly higher than the lowest achievable ones with sideband resolved cooling methods.

We present the exact theory of quantum engines whose working medium is a network of driven oscillators performing an arbitrary cyclic process while coupled to thermal and nonthermal reservoirs. We show that when coupled to a single reservoir work cannot be extracted unless there is population inversion, and prove that the ratio between the heat flowing out and into the working medium cannot be arbitrarily small, satisfying a form of Clausius inequality. We use such identity to prove that the efficiency of linear quantum engines satisfies a generalized bound, which coincides with the Carnot limit for thermal reservoirs. The previous results enable us to estimate the cost of preparing nonthermal reservoirs, which, if available, could be used to violate the Carnot limit.