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Stochastic thermodynamics of rapidly driven quantum systems, Bulnes Cuetara, Gregory ; ; Esposito, Massimiliano in New Journal of Physics (2015), 17 We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified ... [more ▼] We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the Floquet basis. Transition rates are shown to satisfy the local detailed balance involving the entropy flowing out of the reservoirs. The first and second law of thermodynamics are also identified at the trajectory level. Mechanical work is identified by means of initial and final projections on energy eigenstates of the system. We explicitly show that this two step measurement becomes unnecessary in the long time limit. A steady-state fluctuation theorem for the currents and rate of mechanical work is also established. This relation does not require the introduction of a time reversed external driving which is usually needed when considering systems subjected to time asymmetric external fields. This is understood as a consequence of the secular approximation applied in consistency with the large time scale separation between the fast driving oscillations and the slower relaxation dynamics induced by the environment. Our results are finally illustrated on a model describing a thermodynamic engine. [less ▲] Detailed reference viewed: 181 (12 UL)Efficiency fluctuations in quantum thermoelectric devices Esposito, Massimiliano ; ; 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 ▲] Detailed reference viewed: 160 (9 UL)Nature of heat in strongly coupled open quantum systems Esposito, Massimiliano ; ; in Physical Review B - Condensed Matter and Materials Physics (2015), 92(23), We show that any heat definition expressed as an energy change in the reservoir energy plus any fraction of the system-reservoir interaction is not an exact differential when evaluated along reversible ... [more ▼] We show that any heat definition expressed as an energy change in the reservoir energy plus any fraction of the system-reservoir interaction is not an exact differential when evaluated along reversible isothermal transformations, except when that fraction is zero. Even in that latter case the reversible heat divided by temperature, namely entropy, does not satisfy the third law of thermodynamics and diverges in the low temperature limit. These results are found within the framework of nonequilibrium Green functions (NEGF) using a single level quantum dot strongly coupled to fermionic reservoirs and subjected to a time-dependent protocol modulating the dot energy as well as the dot-reservoir coupling strength. © 2015 American Physical Society. [less ▲] Detailed reference viewed: 139 (5 UL)Efficiency Statistics at All Times: Carnot Limit at Finite Power Polettini, Matteo ; Verley, Gatien ; Esposito, Massimiliano 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 ▲] Detailed reference viewed: 213 (8 UL)Double quantum dot coupled to a quantum point contact: A stochastic thermodynamics approach ; Esposito, Massimiliano in New Journal of Physics (2015), 17(9), We study the nonequilibrium properties of an electronic circuit composed of a double quantum dot (DQD) channel capacitively coupled to a quantum point contact (QPC) within the framework of stochastic ... [more ▼] We study the nonequilibrium properties of an electronic circuit composed of a double quantum dot (DQD) channel capacitively coupled to a quantum point contact (QPC) within the framework of stochastic thermodynamics. We show that the transition rates describing the dynamics satisfy a nontrivial local detailed balance and that the statistics of energy and particle currents across both channels obeys a fluctuation theorem. We analyze two regimes where the device operates as a thermodynamic machine and study its output power and efficiency fluctuations. We show that the electrons tunneling through the QPC without interacting with the DQD have a strong effect on the device efficiency. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. [less ▲] Detailed reference viewed: 154 (4 UL)Kinetics and thermodynamics of reversible polymerization in closed systems ; ; Esposito, Massimiliano et al 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 ▲] Detailed reference viewed: 127 (4 UL)Stochastic thermodynamics of hidden pumps Esposito, Massimiliano ; 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 ▲] Detailed reference viewed: 114 (6 UL)Thermodynamics of the polaron master equation at finite bias ; ; Esposito, Massimiliano et al in Journal of Chemical Physics (2015), 142(13), We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating ... [more ▼] We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system. (C) 2015 AIP Publishing LLC. [less ▲] Detailed reference viewed: 125 (10 UL)Ensemble and trajectory thermodynamics: A brief introduction ; Esposito, Massimiliano in Physica a-Statistical Mechanics and Its Applications (2015), 418 We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir. (C) 2014 Elsevier B.V. All rights reserved. Detailed reference viewed: 150 (8 UL)Quantum Thermodynamics: A Nonequilibrium Green's Function Approach Esposito, Massimiliano ; ; 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 ▲] Detailed reference viewed: 180 (12 UL)Dissipation in noisy chemical networks: The role of deficiency Esposito, Massimiliano ; Polettini, Matteo ; Wachtel, Artur in Journal of Chemical Physics (2015), 145(18), 184103 We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known ... [more ▼] We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of complex behavior such as multistability and oscillations, is shown to also characterize the entropic balance. In particular, when deficiency is zero the average stochastic dissipation rate equals that of the corresponding deterministic model, where correlations are disregarded. In fact, dissipation can be reduced by the effect of noise, as occurs in a toy model of metabolism that we employ to illustrate our findings. This phenomenon highlights that there is a close interplay between deficiency and the activation of new dissipative pathways at low molecule numbers [less ▲] Detailed reference viewed: 243 (22 UL)Work statistics in stochastically driven systems Verley, Gatien ; ; Esposito, Massimiliano 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 ▲] Detailed reference viewed: 144 (9 UL)Thermodynamics with Continuous Information Flow ; Esposito, Massimiliano in Physical Review X (2014), 4 as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is <br />continuously generated in an auxiliary system and then transferred to a relevant system that can ... [more ▼] as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is <br />continuously generated in an auxiliary system and then transferred to a relevant system that can utilize it to <br />fuel otherwise impossible processes. Indeed, while the joint system satisfies the second law, the entropy <br />balance for the relevant system is modified by an information term related to the mutual information rate <br />between the two systems. We show that many important results previously derived for nonautonomous <br />Maxwell demons can be recovered from our formalism and use a cycle decomposition to analyze the <br />continuous information flow in autonomous systems operating at a steady state. A model system is used to <br />illustrate our findings. [less ▲] Detailed reference viewed: 474 (123 UL)The unlikely Carnot efficiency Verley, Gatien ; Esposito, Massimiliano ; et al 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 ▲] Detailed reference viewed: 375 (125 UL)Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws Polettini, Matteo ; Esposito, Massimiliano in Journal of Chemical Physics (2014), 141 chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is ... [more ▼] chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = sY between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats sY. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg’s theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction. [less ▲] Detailed reference viewed: 306 (14 UL)Exact fluctuation theorem without ensemble quantities Bulnes Cuetara, Gregory ; Esposito, Massimiliano ; 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 ▲] Detailed reference viewed: 183 (13 UL)Mutual entropy production in bipartite systems Diana, Giovanni ; Esposito, Massimiliano in Journal of Statistical Mechanics : Theory and Experiment (2014) It was recently shown by Barato et al (2013 Phys. Rev. E 87 042104) that the mutual information at the trajectory level of a bipartite Markovian system is not bounded by the entropy production. In the ... [more ▼] It was recently shown by Barato et al (2013 Phys. Rev. E 87 042104) that the mutual information at the trajectory level of a bipartite Markovian system is not bounded by the entropy production. In the same way as Gaspard showed (2004 J. Stat. Phys. 117 599) that the entropy production is not directly related to the Shannon entropy at the trajectory level but is in fact equal to its difference from the so-called time-reversed Shannon entropy, we show in this paper that the difference between the mutual information and its time-reversed form is equal to the mutual entropy production (MEP), i.e. the difference between the full entropy production and that of the two marginal processes. Evaluation of the MEP is in general a difficult task due to non-Markovian effects. For bipartite systems, we provide closed expressions in various limiting regimes which we verify by numerical simulations. [less ▲] Detailed reference viewed: 139 (6 UL)Transient fluctuation theorems for the currents and initial equilibrium ensembles Polettini, Matteo ; Esposito, Massimiliano in Journal of Statistical Mechanics: Theory and Experiment (2014) Detailed reference viewed: 16 (3 UL)Universal theory of efficiency fluctuations ; ; et al in Physical Review E (2014), 90(5), Detailed reference viewed: 160 (6 UL)Thermodynamics of quantum-jump-conditioned feedback control ; ; et al 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 ▲] Detailed reference viewed: 199 (5 UL) |
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