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Irreversibility is a fundamental concept with important implications at many levels. It pinpoints the fundamental difference between the intrinsically reversible microscopic equations of motion and the unidirectional arrow of time that emerges at the macroscopic level. More pragmatically, a full quantification of the degree of irreversibility of a given process can help in the characterisation of the performance of thermo-machines operating at the quantum level. Here, we review the concept of entropy production, which is commonly intended as {\it the} measure of thermodynamic irreversibility of a process, pinpointing the features and shortcomings of its current formulation., Comment: 8 pages, no figure, RevTeX4-1. To appear as a chapter of "Thermodynamics in the quantum regime - Recent Progress and Outlook", F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso eds., Springer International Publishing

Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility on a non-equilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time-reverse. Our result addresses the concept of irreversibility from a microscopic quantum standpoint., Comment: 8 pages, 7 figures, RevTeX4-1; Accepted for publication Phys. Rev. Lett

In this paper we present a method to derive an exact master equation for a bosonic system coupled to a set of other bosonic systems, which plays the role of the reservoir, under the strong coupling regime, i.e., without resorting to either the rotating-wave or secular approximations. Working with phase-space distribution functions, we verify that the dynamics are separated in the evolution of its center, which follows classical mechanics, and its shape, which becomes distorted. This is the generalization of a result by Glauber, who stated that coherent states remain coherent under certain circumstances, specifically when the rotating-wave approximation and a zero-temperature reservoir are used. We show that the counter-rotating terms generate fluctuations that distort the vacuum state, much the same as thermal fluctuations.Finally, we discuss conditions for non-Markovian dynamics.

We present a fully quantum scheme to perform 2D atomic lithography based on a cross-cavity optical Stern-Gerlach setup: an array of two mutually orthogonal cavities crossed by an atomic beam perpendicular to their optical axes, which is made to interact with two identical modes. After deriving an analytical solution for the atomic momentum distribution, we introduce a protocol allowing us to control the atomic deflection by manipulating the amplitudes and phases of the cavity field states.