Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach

in Physical Review. E. (2013), 88

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general ... [more ▼]

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold. However, we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur, making concave transients extremely short lived with respect to the main relaxation modes. We describe a general method based on the Fisher information matrix to discriminate between generators that admit nonconvex solutions and those that do not. While initial conditions leading to concave transients are shown to be extremely fine-tuned, by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state. Convexity does occur when the system is close to satisfying detailed balance or, more generally, when certain normality conditions of the decay modes are satisfied. Our results circumscribe the range of validity of a conjecture by Maes et al. [ Phys. Rev. Lett. 107 010601 (2011)] regarding monotonicity of the large deviation rate functional for the occupation probability, showing that while the conjecture might hold in the long-time limit, the conditions for Lyapunov's second criterion for stability are not met. [less ▲]

Entropy production in quantum Brownian motion

in Journal of Statistical Mechanics: Theory and Experiment (2013), P04005

We investigate how to coherently define entropy production for a process of transient relaxation in the quantum Brownian motion model for the harmonic potential. We compare a form, referred to as ‘poised’ ... [more ▼]

We investigate how to coherently define entropy production for a process of transient relaxation in the quantum Brownian motion model for the harmonic potential. We compare a form, referred to as ‘poised’ (P), which after non-Markovian transients corresponds to a definition of heat as the change in the system Hamiltonian of mean force, with a recent proposal by Esposito et al (ELB) based on a definition of heat as the energy change in the bath. Both expressions yield a positive-definite entropy production and they coincide for vanishing coupling strength, but their difference is proved to be always positive (after non-Markovian transients disappear) and to grow as the coupling strength increases. In the classical ver-damped limit the ‘poised’ entropy production converges to the entropy production used in stochastic thermodynamics. We also investigate the effects of the system size, and of the ensuing Poincar´e recurrences, and how the classical limit is approached. We close by discussing the strongcoupling limit, in which the ideal canonical equilibrium of the bath is violated. [less ▲]

Thermodynamics of a Physical Model Implementing a Maxwell Demon

in Physical Review Letters (2013), 110(4)(040601(5)), 040601-1

We present a physical implementation of a Maxwell demon which consists of a conventional single electron transistor (SET) capacitively coupled to another quantum dot detecting its state. Altogether, the ... [more ▼]

We present a physical implementation of a Maxwell demon which consists of a conventional single electron transistor (SET) capacitively coupled to another quantum dot detecting its state. Altogether, the system is described by stochastic thermodynamics. We identify the regime where the energetics of the SET is not affected by the detection, but where its coarse-grained entropy production is shown to contain a new contribution compared to the isolated SET. This additional contribution can be identified as the information flow generated by the ‘‘Maxwell demon’’ feedback in an idealized limit. [less ▲]

Modulated two-level system: Exact work statistics

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2013), 88

We consider an open two-level system driven by a piecewise constant periodic field and described by a rate equation with Fermi, Bose, and Arrhenius rates, respectively. We derive an analytical expression ... [more ▼]

We consider an open two-level system driven by a piecewise constant periodic field and described by a rate equation with Fermi, Bose, and Arrhenius rates, respectively. We derive an analytical expression for the generating function and large deviation function of the work performed by the field and show that a work fluctuation theorem holds. [less ▲]

Stochastically driven single-level quantum dot: A nanoscale finite-time thermodynamic machine and its various operational modes

in Physical Review. E. (2012), 85(3),

We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two ... [more ▼]

We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two values. In the isothermal regime, it can operate as a rechargeable battery by generating an electric current against the applied bias in response to the stochastic driving and then redelivering work in the reverse cycle. This behavior is reminiscent of the Parrondo paradox. If there is a thermal gradient the device can function as a work-generating thermal engine or as a refrigerator that extracts heat from the cold reservoir via the work input of the stochastic driving. The efficiency of the machine at maximum power output is investigated for each mode of operation, and universal features are identified. [less ▲]

Stochastic thermodynamics under coarse graining

in Physical Review. E. (2012), 85(4),

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of “mesostates” (e.g., sets ... [more ▼]

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of “mesostates” (e.g., sets of “microstates”), the consequence on the thermodynamic description of the system is studied in detail. When microstates within mesostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the mesostate level. This is not the case when these microstates remain out of equilibrium, leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots. [less ▲]

Nonequilibrium Thermodynamics and Nose-Hoover Dynamics

in Journal of Physical Chemistry B (2011), 115(18),

We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed ... [more ▼]

We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical equilibrium. By treating the “real” variables as the system and the thermostatted variable as the reservoir, we establish the first and second law of thermodynamics. As for Hamiltonian systems, the entropy production can be expressed as a relative entropy measuring the system-reservoir correlations established during the dynamics. [less ▲]

Second law and Landauer principle far from equilibrium

in Epl (2011), 95(4),

The amount of work that is needed to change the state of a system in contact <br /><br />with a heat bath between specified initial and final nonequilibrium states is at least equal to the <br /><br ... [more ▼]

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

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

in Physical Review. E. (2010), 82(1),

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 ... [more ▼]

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. [less ▲]

Quantum-dot Carnot engine at maximum power

in Physical Review. E. (2010), 81(4),

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 ... [more ▼]

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. [less ▲]