Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle

We study driven finite quantum systems in contact with a thermal reservoir in the regime in which the system changes slowly in comparison to the equilibration time. The associated isothermal adiabatic theorem allows us to control the full statistics of energy transfers in quasi-static processes. Within this approach, we extend Landauer's Principle on the energetic cost of erasure processes to the level of the full statistics and elucidate the nature of the fluctuations breaking Landauer's bound.Comment: 24 pages, 4 figures; In the new version, Section 4 contains an extended discussion of the violation of Landauer's boun

Full statistics of energy conservation in two times measurement protocols

The first law of thermodynamics states that the average total energy current between different reservoirs vanishes at large times. In this note we examine this fact at the level of the full statistics of two times measurement protocols also known as the Full Counting Statistics. Under very general conditions, we establish a tight form of the first law asserting that the fluctuations of the total energy current computed from the energy variation distribution are exponentially suppressed in the large time limit. We illustrate this general result using two examples: the Anderson impurity model and a 2D spin lattice model.Comment: 5 pages, 1 figure. Accepted for publication in Phys. Rev.

Quantum trajectory of the one atom maser

The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states which is called a quantum trajectory. In this paper we consider a specific model of such a quantum trajectory associated to the one-atom maser model. It describes the evolution of one mode of the quantized electromagnetic field in a cavity interacting with two-level atoms. When the system is non-resonant we prove that this Markov chain admits a unique invariant probability measure. We moreover prove convergence in the Wasserstein metric towards this invariant measure. These results rely on a purification theorem: almost surely the state of the system approaches the set of pure states. Compared to similar results in the literature, the system considered here is infinite dimensional. While existence of an invariant measure is a consequence of the compactness of the set of states in finite dimension, in infinite dimension existence of an invariant measure is not free. Furthermore usual purification criterions in finite dimension have no straightforward equivalent in infinite dimension

Control of fluctuations and heavy tails for heat variation in the two-time measurement framework

We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in a complex neighborhood of 0. On a set of canonical examples, with bounded and unbounded perturbations, we show that our ultraviolet conditions are essentially necessary. If the form factor of the perturbation does not meet our assumptions, the heat variation distribution exhibits heavy tails. The tails can be as heavy as preventing the existence of a fourth moment of the heat variation

A note on two-times measurement entropy production and modular theory

Recent theoretical investigations of the two-times measurement entropy production (2TMEP) in quantum statistical mechanics have shed a new light on the mathematics and physics of the quantum-mechanical probabilistic rules. Among notable developments are the extensions of entropic fluctuation relations to quantum domain and discovery of a deep link between 2TMEP and modular theory of operator algebras. All these developments concerned the setting where the state of the system at the instant of the first measurement is the same as the state whose entropy production is measured. In this work we consider the case where these two states are different and link this more general 2TEMP to modular theory. The established connection allows us to show that under general ergodicity assumptions the 2TEMP is essentially independent of the choice of the system state at the instant of the first measurement due to a decoherence effect induced by the first measurement. This stability sheds a new light on the concept of quantum entropy production, and, in particular, on possible quantum formulations of the celebrated classical Gallavotti--Cohen Fluctuation Theorem which will be studied in the continuation of this work