Efficiency fluctuations in quantum thermoelectric devices

in Physical Review. B (2015), 91(11),

We present a method, based on characterizing efficiency fluctuations, to assess the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions ... [more ▼]

We present a method, based on characterizing efficiency fluctuations, to assess the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions, namely, stochasticity in the junction's performance, quantum effects, and nonequilibrium features preventing a linear response analysis. It is based on a nonequilibrium Green's function (NEGF) approach, which we use to derive the full counting statistics (FCS) for heat and work, and which in turn allows us to calculate the statistical properties of efficiency fluctuations. We simulate the latter for a variety of simple models where our method is exact. By analyzing the discrepancies with the semiclassical prediction of a quantum master equation (QME) approach, we emphasize the quantum nature of efficiency fluctuations for realistic junction parameters. We finally propose an approximate Gaussian method to express efficiency fluctuations in terms of nonequilibrium currents and noises which are experimentally measurable in molecular junctions. [less ▲]

Stochastic thermodynamics of hidden pumps

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2015), 91(5),

We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping ... [more ▼]

We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping mechanism is not accessible, will observe a Markov chain satisfying local detailed balance with an emerging effective force induced by the hidden pump. Due to the reversibility of the pump, the actual entropy production turns out to be lower than the coarse-grained entropy production estimated from the flows and affinities of the resulting Markov chain. Moreover, in presence of a large time scale separation between the fast-pumping dynamics and the slow-network dynamics, a finite current with zero dissipation may be produced. We make use of these general results to build a synthetase-like kinetic scheme able to reversibly produce high free-energy molecules at a finite rate and a rotatory motor achieving 100% efficiency at finite speed. © 2015 American Physical Society. [less ▲]

Efficiency Statistics at All Times: Carnot Limit at Finite Power

in Physical Review Letters (2015), 114(5),

We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter ... [more ▼]

We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter zeta. It has a peculiar behavior: no moments, one sub-, and one super-Carnot maxima corresponding to reverse operating regimes (engine or pump), the most probable efficiency decreasing in time. The limit zeta -> 0 where the Carnot bound can be saturated gives rise to two extreme situations, one where the machine works at its macroscopic efficiency, with Carnot limit corresponding to no entropy production, and one where for a transient time scaling like 1/zeta microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches the Carnot limit at finite entropy production. [less ▲]

Kinetics and thermodynamics of reversible polymerization in closed systems

in New Journal of Physics (2015), 17(8),

Motivated by a recent study on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer ... [more ▼]

Motivated by a recent study on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer concentration and the other one not. The chemical kinetics is described by rate equations following the mass-action law. We consider a closed system and nonequilibrium initial conditions and show that the system dynamically evolves towards equilibrium where a detailed balance is satisfied. The entropy production during this process can be expressed as the time derivative of a Lyapunov function. When the solvent is not included in the description and the dynamics conserves the total concentration of polymer, the Lyapunov function can be expressed as a Kullback-Leibler divergence between the nonequilibrium and the equilibrium polymer length distribution. The same result holds true when the solvent is explicitly included in the description and the solution is assumed dilute, whether or not the total polymer concentration is conserved. Furthermore, in this case a consistent nonequilibrium thermodynamic formulation can be established and the out-of-equilibrium thermodynamic enthalpy, entropy and free energy can be identified. Such a framework is useful in complementing standard kinetics studies with the dynamical evolution of thermodynamic quantities during polymerization. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. [less ▲]

Quantum Thermodynamics: A Nonequilibrium Green's Function Approach

in Physical Review Letters (2015), 114(8),

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium ... [more ▼]

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit. [less ▲]

Work statistics in stochastically driven systems

in New Journal of Physics (2014), 16

We identify the conditions under which a stochastic driving that induces energy changes into a system coupled with a thermal bath can be treated as a work source. When these conditions are met, the work ... [more ▼]

We identify the conditions under which a stochastic driving that induces energy changes into a system coupled with a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfy the Crooks fluctuation theorem traditionally derived for deterministic drivings. We illustrate this fact by calculating and comparing the work statistics for a two-level system driven respectively by a stochastic and a deterministic piecewise constant protocol. [less ▲]

The unlikely Carnot efficiency

in Nature Communications (2014)

The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a ... [more ▼]

The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It led to the discovery of the second law and to the definition of the Kelvin temperature scale. Small-scale engines operate in the presence of highly fluctuating input and output energy fluxes. They are therefore much better characterized by fluctuating efficiencies. In this study, using the fluctuation theorem, we identify universal features of efficiency fluctuations. While the standard thermodynamic efficiency is, as expected, the most likely value, we find that the Carnot efficiency is, surprisingly, the least likely in the long time limit. Furthermore, the probability distribution for the efficiency assumes a universal scaling form when operating close-to-equilibrium. We illustrate our results analytically and numerically on two model systems. [less ▲]

Exact fluctuation theorem without ensemble quantities

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2014), 1402

Evaluating the entropy production (EP) along a stochastic trajectory requires the knowledge of the system probability distribution, an ensemble quantity notoriously difficult to measure. In this letter ... [more ▼]

Evaluating the entropy production (EP) along a stochastic trajectory requires the knowledge of the system probability distribution, an ensemble quantity notoriously difficult to measure. In this letter, we show that the EP of nonautonomous systems in contact with multiple reservoirs can be expressed solely in terms of physical quantities measurable at the single trajectory level with a suitable preparation of the initial condition. As a result, we identify universal energy and particle fluctuation relations valid for any measurement time. We apply our findings to an electronic junction model which may be used to verify our prediction experimentally. [less ▲]

Transient fluctuation theorems for the currents and initial equilibrium ensembles

in Journal of Statistical Mechanics: Theory and Experiment (2014)

Thermodynamics of quantum-jump-conditioned feedback control

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2013), 88(062107),

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic ... [more ▼]

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states. [less ▲]