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See detailIrreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws
Polettini, Matteo UL; Esposito, Massimiliano UL

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 ▲]

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See detailExact fluctuation theorem without ensemble quantities
Bulnes Cuetara, Gregory UL; Esposito, Massimiliano UL; Imparato, Alberto

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 ▲]

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See detailMutual entropy production in bipartite systems
Diana, Giovanni UL; Esposito, Massimiliano UL

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 ▲]

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See detailTransient fluctuation theorems for the currents and initial equilibrium ensembles
Polettini, Matteo UL; Esposito, Massimiliano UL

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

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See detailUniversal theory of efficiency fluctuations
Verley, Gatien; Willaert, Tim; Van den Broeck, Christian et al

in Physical Review. E. (2014), 90(5),

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See detailThermodynamics of quantum-jump-conditioned feedback control
Strasberg, P.; Schaller, G.; Brandes, T. 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 ▲]

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See detailEffective fluctuation theorems for electron transport in a double quantum dot coupled to a quantum point contact
Bulnes Cuetara, Gregory UL; Esposito, Massimiliano UL; Schaller, Gernot et al

in Physical Review. B, Condensed Matter (2013), 88(115134),

A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD) capacitively coupled to a quantum point contact (QPC) for the measurement of the DQD charge state ... [more ▼]

A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD) capacitively coupled to a quantum point contact (QPC) for the measurement of the DQD charge state. Starting from a Hamiltonian model, a master equation is obtained for the stochastic process taking place in the DQD while the QPC is at or away from equilibrium, allowing us to study the measurement back-action of the QPC onto the DQD. The QPC is treated nonperturbatively in our analysis. Effective fluctuation theorems are established for the full counting statistics of the DQD current under different limiting conditions. These fluctuation theorems hold with respect to an effective affinity characterizing the nonequilibrium environment of the DQD and differing from the applied voltage if the QPC is out of equilibrium. The effective affinity may even change its sign if the Coulomb drag of the QPC reverses the DQD current. The thermodynamic implications of the effective fluctuation theorems are discussed. [less ▲]

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See detailNonconvexity of the relative entropy for Markov dynamics: A Fisher information approach
Polettini, Matteo UL; Esposito, Massimiliano UL

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 ▲]

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See detailEntropy-generated power and its efficiency
Golubeva, N.; Imparato, A.; Esposito, Massimiliano UL

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2013), 88(042105),

We propose a simple model for a motor that generates mechanical motion by exploiting an entropic force arising from the topology of the underlying phase space. We show that the generation of mechanical ... [more ▼]

We propose a simple model for a motor that generates mechanical motion by exploiting an entropic force arising from the topology of the underlying phase space. We show that the generation of mechanical forces in our system is surprisingly robust to local changes in kinetic and topological parameters. Furthermore, we find that the efficiency at maximum power may show discontinuities. [less ▲]

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See detailEntropy production in quantum Brownian motion
Pucci, Lorenzo; Esposito, Massimiliano UL; Peliti, Luca

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 ▲]

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See detailSingle-electron transistor strongly coupled to vibrations: counting statistics and fluctuation theorem
Schaller, Gernot; Krause, Thilo; Brandes, Tobias et al

in New Journal of Physics (2013), 033032

Using a simple quantum master equation approach, we calculate the full counting statistics of a single-electron transistor strongly coupled to vibrations. The full counting statistics contains both the ... [more ▼]

Using a simple quantum master equation approach, we calculate the full counting statistics of a single-electron transistor strongly coupled to vibrations. The full counting statistics contains both the statistics of integrated particle and energy currents associated with the transferred electrons and phonons. A universal as well as an effective fluctuation theorem are derived for the general case where the various reservoir temperatures and chemical potentials are different. The first relates to the entropy production generated in the junction, while the second reveals internal information of the system. The model recovers the Franck–Condon blockade, and potential applications to noninvasive molecular spectroscopy are discussed. [less ▲]

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See detailThermodynamics of a Physical Model Implementing a Maxwell Demon
Strasberg, Philipp; Schaller, Gernot; Brandes, Tobias et al

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 ▲]

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See detailFinite-time erasing of information stored in fermionic bits
Diana, Giovanni UL; Bagci, G. Baris; Esposito, Massimiliano UL

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

We address the issue of minimizing the heat generated when erasing the information stored in an array of quantum dots in finite time. We identify the fundamental limitations and trade-offs involved in ... [more ▼]

We address the issue of minimizing the heat generated when erasing the information stored in an array of quantum dots in finite time. We identify the fundamental limitations and trade-offs involved in this process and analyze how a feedback operation can help improve it [less ▲]

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See detailModulated two-level system: Exact work statistics
Verley, Gatien UL; Van den Broeck, C.; Esposito, Massimiliano UL

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 ▲]

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See detailStochastic thermodynamics for “Maxwell demon” feedbacks
Esposito, Massimiliano UL; Schaller, Gernot

in Europhysics Letters (2012), 99(30003),

We propose a way to incorporate the effect of a specific class of feedback processes into <br /><br />stochastic thermodynamics. These “Maxwell demon” feedbacks do not affect the system energetics <br ... [more ▼]

We propose a way to incorporate the effect of a specific class of feedback processes into <br /><br />stochastic thermodynamics. These “Maxwell demon” feedbacks do not affect the system energetics <br /><br />but only the energy barriers between the system states (in a way which depends on the system <br /><br />states). They are thus of a purely informational nature. We show that the resulting formalism can <br /><br />be applied to study the thermodynamic effect of a feedback process acting on electron transfers <br /><br />through a junction. [less ▲]

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See detailStochastically driven single-level quantum dot: A nanoscale finite-time thermodynamic machine and its various operational modes
Esposito, Massimiliano UL; Kumar, Niraj; Lindenberg, Katja et al

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 ▲]

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See detailStochastic thermodynamics under coarse graining
Esposito, Massimiliano UL

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 ▲]

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See detailFinite-time erasing of information stored in fermionic bits
Diana, Giovanni UL; Bagci, G. Baris; Esposito, Massimiliano UL

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2012), 87(1), 012111

We address the issue of minimizing the heat generated when erasing the information stored in an array of quantum dots in finite time. We identify the fundamental limitations and trade-offs involved in ... [more ▼]

We address the issue of minimizing the heat generated when erasing the information stored in an array of quantum dots in finite time. We identify the fundamental limitations and trade-offs involved in this process and analyze how a feedback operation can help improve it. [less ▲]

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See detailFluctuation theorems for capacitively coupled electronic currents
Cuetara, Gregory Bulnes; Esposito, Massimiliano UL; Gaspard, Pierre

in Physical Review. B (2011), 84(16),

The counting statistics of electron transport is studied theoretically in a system with two capacitively coupled parallel transport channels. Each channel is composed of a quantum dot connected by ... [more ▼]

The counting statistics of electron transport is studied theoretically in a system with two capacitively coupled parallel transport channels. Each channel is composed of a quantum dot connected by tunneling to two reservoirs. The nonequilibrium steady state of the system is controlled by two affinities or thermodynamic forces, each one determined by the two reservoirs of each channel. The status of a single-current fluctuation theorem is investigated starting from the fundamental two-current fluctuation theorem, which is a consequence of microreversibility.We show that the single-current fluctuation theorem holds in the limit of a large Coulomb repulsion between the two parallel quantum dots, as well as in the limit of a large current ratio between the parallel channels. In this latter limit, the symmetry relation of the single-current fluctuation theorem is satisfied with respect to an effective affinity that is much lower than the affinity determined by the reservoirs. This backaction effect is characterized quantitatively. [less ▲]

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See detailNonequilibrium Thermodynamics and Nose-Hoover Dynamics
Esposito, Massimiliano UL; Monnai, Takaaki

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 ▲]

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