Massimiliano Esposito

Spin relaxation in a complex environment

We report the study of a model of a two-level system interacting in a nondiagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its consequences on the dynamics of the two-level system is analyzed. We show the existence of a critical value of the interaction, depending on the mean level spacing of the environment, above which the dynamics is self-averaging and closely obey a master equation for the time evolution of the observables of the two-level system. Analytic results are also obtained in the strong coupling regimes. We finally study the equilibrium values of the two-level system population and show under which condition it thermalizes to the environment temperature.

Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems

Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Greens functions techniques for computing the energy and particle statistics are presented.

Efficiency at Maximum Power of Low-Dissipation Carnot Engines

We study the efficiency at maximum power, η*, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For engines reaching Carnot efficiency ηC=1-Tc/Th in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that η* is bounded from above by ηC/(2-ηC) and from below by ηC/2. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend, respectively, to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency ηCA=1-√Tc/Th] is recovered.

Thermoelectric efficiency at maximum power in a quantum dot

We identify the operational conditions for maximum power of a nanothermoelectric engine consisting of a single quantum level embedded between two leads at different temperatures and chemical potentials. The corresponding thermodynamic efficiency agrees with the Curzon-Ahlborn expression up to quadratic terms in the gradients, supporting the thesis of universality beyond linear response.

Second law and Landauer principle far from equilibrium

The amount of work that is needed to change the state of a system in contact with a heat bath between specified initial and final nonequilibrium states is at least equal to the corresponding equilibrium free energy difference plus (respectively, minus) temperature times the information of the final (respectively, the initial) state relative to the corresponding equilibrium distributions.

Quantum master equation for electron transport through quantum dots and single molecules

A quantum master equation QME is derived for the many-body density matrix of an open current-carrying system weakly-coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of the number of electrons in the system. We show that coherences between system states with different number of electrons, n Fock space coherences, do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order of or faster than the system Bohr frequencies. For large bias, when all the system many-body states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation when the damping is slow compared to the Bohr frequencies, the dynamics of populations and coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.

Three faces of the second law. I. Master equation formulation

We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second-law-like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach.

Entropy production as correlation between system and reservoir

We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs, each of which is initially described by a canonical equilibrium distribution. Although the total entropy of system plus reservoirs is conserved, we show that system entropy production is always positive and is a direct measure of system–reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our novel interpretation of the Second Law in a microscopically reversible finite-size setting, with strong coupling between the system and the reservoirs. With this model, we also explicitly show the approach of our exact formulation to the standard description of irreversibility in the limit of a large reservoir.

Quantum-dot Carnot engine at maximum power.

We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.

Thermodynamics with Continuous Information Flow

We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is continuously generated in an auxiliary system and then transferred to a relevant system that can utilize it to fuel otherwise impossible processes. Indeed, while the joint system satisfies the second law, the entropy balance for the relevant system is modified by an information term related to the mutual information rate between the two systems. We show that many important results previously derived for nonautonomous Maxwell demons can be recovered from our formalism and use a cycle decomposition to analyze the continuous information flow in autonomous systems operating at steady-state. A model system is used to illustrate our findings.