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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: 161 (7 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: 93 (9 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: 323 (125 UL)Energy versus Information Based Estimations of Dissipation Using a Pair of Magnetic Colloidal Particles ; ; Verley, Gatien et al in Physical Review Letters (2014), 112(18), 180604 Using the framework of stochastic thermodynamics, we present an experimental study of a doublet of magnetic colloidal particles that is manipulated by a time-dependent magnetic field. Because of ... [more ▼] Using the framework of stochastic thermodynamics, we present an experimental study of a doublet of magnetic colloidal particles that is manipulated by a time-dependent magnetic field. Because of hydrodynamic interactions, each bead experiences a state-dependent friction, which we characterize using a hydrodynamic model. In this work, we compare two estimates of the dissipation in this system: the first one is energy based since it relies on the measured interaction potential, while the second one is information based since it uses only the information content of the trajectories. While the latter only offers a lower bound of the former, we find it to be simple to implement and of general applicability to more complex systems. [less ▲] Detailed reference viewed: 70 (3 UL)Modulated two-level system: Exact work statistics Verley, Gatien ; ; Esposito, Massimiliano 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 ▲] Detailed reference viewed: 95 (7 UL)Inequalities Generalizing the Second Law of Thermodynamics for Transitions between Non-stationary States Verley, Gatien ; ; in Physical Review Letters (2012), 108 We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution ... [more ▼] We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and nonadiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law-like inequalities for transitions between nonstationary states. [less ▲] Detailed reference viewed: 48 (1 UL)Fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium Verley, Gatien ; in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2012), 86 We present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time ... [more ▼] We present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time-dependent perturbation. By assumption, the evolution of the system must be described by Markovian dynamics. We distinguish two different situations depending on the way the nonequilibrium state is prepared; either it is created by some driving or it results from a relaxation following some initial nonstationary conditions. Our approach is based on a recent generalization of the Hatano-Sasa relation for nonstationary probability distributions. We also investigate whether a form of the second law holds for separate parts of the entropy production and for any nonstationary reference process, a question motivated by the work of M. Esposito et al. [ Phys. Rev. Lett. 104 090601 (2010)]. We find that although the special structure of the theorems derived in this reference is not recovered in the general case, detailed fluctuation theorems still hold separately for parts of the entropy production. These detailed fluctuation theorems contain interesting generalizations of the second law of thermodynamics for nonequilibrium systems. [less ▲] Detailed reference viewed: 47 (0 UL)Fluctuations and response from a Hatano and Sasa approach Verley, Gatien ; in Physica Scripta (2012), 86(5), 058505 In this commentary paper, we present some of the main ideas on deriving a modified fluctuation-dissipation theorem off equilibrium, which in the end can all be related to an approach based on a ... [more ▼] In this commentary paper, we present some of the main ideas on deriving a modified fluctuation-dissipation theorem off equilibrium, which in the end can all be related to an approach based on a generalized Hatano-Sasa relation. This generalized Hatano?Sasa relation also contains an interesting inequality, which can be viewed as a generalization of the second law of thermodynamics to transitions between non-equilibrium states. [less ▲] Detailed reference viewed: 43 (0 UL)Modified fluctuation-dissipation theorem for non-equilibrium steady states and applications to molecular motors Verley, Gatien ; ; in Europhysics Letters [=EPL] (2011), 93(1), 10002 We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady states and obeying Markovian dynamics. We discuss the ... [more ▼] We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady states and obeying Markovian dynamics. We discuss the interpretation of this result in terms of trajectory entropy excess. The framework is illustrated on a simple pedagogical example of a molecular motor. We also derive in this context generalized Green-Kubo relations similar to the ones obtained recently in Seifert U., Phys. Rev. Lett., 104 (2010) 138101 for more general networks of biomolecular states. [less ▲] Detailed reference viewed: 49 (0 UL)Fluctuation relations and fluctuation-response for molecular motors Verley, Gatien ; in Garrido, Pedro L.; Marro, Joaquín; de los Santos, F. (Eds.) AIP Conference Proceedings (2011) Fluctuation relations are a set of remarkable relations obeyed by a large class of systems and arbitrarily far from equilibrium. It is interesting to discuss the implications of these relations for ... [more ▼] Fluctuation relations are a set of remarkable relations obeyed by a large class of systems and arbitrarily far from equilibrium. It is interesting to discuss the implications of these relations for molecular motors, which are chemically driven enzymes. These enzymes operate stochastically at the molecular level and for these reasons undergo large thermal fluctuations. Using simple ratchet models of molecular motors, the various forms of fluctuation relations can be illustrated in a simple way. In the linear regime, finite time fluctuation relations imply specific modified fluctuation-dissipation relations. [less ▲] Detailed reference viewed: 21 (1 UL)Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain Verley, Gatien ; ; in Journal of Statistical Mechanics : Theory and Experiment (2011), (10), 10025 In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the ... [more ▼] In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the method for deriving modified fluctuation-dissipation theorems near non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103 090601) is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano?Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy in a way which is similar to what has been done recently in the case of the MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a Brownian particle in a harmonic trap subjected to a quench of temperature and to a time-dependent stiffness; the second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics. [less ▲] Detailed reference viewed: 48 (1 UL) |
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