| Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Raux, P., Goupil, C. and Verley, G. | Thermodynamic circuits: Association of devices in stationary nonequilibrium | 2024 | Phys. Rev. E Vol. 110, pp. 014134 |
article | DOI URL |
| Abstract: For a circuit made of thermodynamic devices in stationary nonequilibrium, we determine the mean currents (of energy, matter, charge, etc.) exchanged with external reservoirs driving the circuit out of equilibrium. Starting from the conductance matrix describing the nonlinear current-force characteristics of each device, we obtain the conductance matrix of the composite device. This generalizes the rule of resistance addition (serial association) or conductance addition (parallel association) in stationary out-of-equilibrium thermodynamics and for multiple coupled potentials and currents of different natures. Our work emphasizes the pivotal role of conservation laws when creating circuits of complex devices. Finally, two examples illustrate among others the determination of the conservation laws for the serial and parallel associations of thermodynamic devices. | |||||
BibTeX:
@article{Raux2024vol110,
author = {Raux, Paul and Goupil, Christophe and Verley, Gatien},
title = {Thermodynamic circuits: Association of devices in stationary nonequilibrium},
journal = {Phys. Rev. E},
publisher = {American Physical Society},
year = {2024},
volume = {110},
pages = {014134},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Raux2024vol110.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Raux2024vol110.pdf},
doi = {https://doi.org/10.1103/PhysRevE.110.014134}
}
|
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| Verley, G. | Nonequilibrium fluctuations and conversion processes | 2024 | School: Université Paris Saclay | phdthesis | URL |
| Abstract: This professorial thesis presents a comprehensive study of conversion processes at the mean and fluctuating levels. It relies on stochastic thermodynamics to model small converters coupling different currents. Large deviation theory provides methodological tools for the presented works, but it is also considered for its profound interplay with statistical physics. The introductory chapter delves into an overall description of my research, zooming into various subfields such as nonequilibrium response theory, fluctuation relations, dynamical phase transitions, Doob transformation, and rectification, or exact computation of cumulant generating function. The second chapter introduces stochastic thermodynamics and the physics of coupled currents in the linear and nonlinear regime at the mean level. We describe the concept of nonlinear conductance and apply this concept to develop a circuit theory of nonequilibrium devices. The third chapter focuses on results in large deviation theory. We extend to level 2.5 the existing relation between large deviations with asymptotically long observation times or asymptotically large activity. In this context, we relate the Doob-transformed processes in continuous and discrete time. Next, we describe the difficulty arising when trying to relate, by Doob transforms, the arrhénius dynamics of in- and out-of-equilibrium systems. We end this chapter by generalizing our work on nonlinear conductance matrices for time-periodic states. The last chapter emphasizes the coherence of our works that aim to characterize the stochastic efficiency of highly fluctuating converters. |
|||||
BibTeX:
@phdthesis{Verley2024volHDR,
author = {Verley, Gatien},
title = {Nonequilibrium fluctuations and conversion processes},
school = {Université Paris Saclay},
year = {2024},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2024volHDR.pdfPDF},
url = {https://theses.hal.science/tel-04719790}
}
|
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| Raux, P., Goupil, C. and Verley, G. | Thermodynamic Circuits 2: Nonequilibrium conductance matrix for a thermoelectric converter | 2024 | Arxiv | article | URL |
| Abstract: Starting from a linear flux-force relation of a thermoelectric material in local equilibrium, we derive non-linear relations between the currents and forces of a thermoelectric converter (TEC) driven far from equilibrium. Our investigation focuses on a one-dimensional TEC of finite thickness. Building on the achievements of the first paper of this series, we unveil the conservation laws governing physical currents (ie linearly dependent currents). Using the latter allows to put forward two relevant bases of physical and fundamental currents. For these bases, we introduce the concept of non equilibrium conductance matrix to describe the current-force relations of a TEC. This concept will be at the core of the third paper of this series in which we illustrate the serial and parallel association on composite TECs. Finally, we determine in a unified way the optimal working points of the TEC in its two operating modes: the electric generator and the heat pump. | |||||
BibTeX:
@article{Raux2024vol,
author = {Paul Raux and Christophe Goupil and Gatien Verley},
title = {Thermodynamic Circuits 2: Nonequilibrium conductance matrix for a thermoelectric converter},
journal = {Arxiv},
year = {2024},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Raux2024.pdf}
}
|
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| Chabane, L., Lazarescu, A. and Verley, G. | Effective Hamiltonians and Lagrangians for Conditioned Markov Processes at Large Volume | 2022 | J. Stat. Phys. Vol. 187(1) |
article | DOI URL |
| Abstract: When analysing statistical systems or stochastic processes, it is often interesting to ask how they behave given that some observable takes some prescribed value. This conditioning problem is well understood within the linear operator formalism based on rate matrices or Fokker-Planck operators, which describes the dynamics of many independent random walkers. Relying on certain spectral properties of the biased linear operators, guaranteed by the Perron-Frobenius theorem, an effective process can be found such that its path probability is equivalent to the conditional path probability. In this paper, we extend those results for nonlinear Markov processes that appear when the many random walkers are no longer independent, and which can be described naturally through a Lagrangian-Hamiltonian formalism within the theory of large deviations at large volume. We identify the appropriate spectral problem as being a Hamilton-Jacobi equation for a biased Hamiltonian, for which we conjecture that two special global solutions exist, replacing the Perron-Frobenius theorem concerning the positivity of the (left and right) dominant eigenvector. We then devise a rectification procedure based on a canonical gauge transformation of the biased Hamiltonian, yielding an effective dynamics in agreement with the original conditioning. Along the way, we present simple examples in support of our conjecture, we examine its consequences on important physical objects such as the fluctuation symmetries of the biased and rectified processes as well as the dual dynamics obtained through time-reversal. We apply all those results to simple independent and interacting models, including a stochastic chemical reaction network and a population process called the Brownian Donkey. | |||||
BibTeX:
@article{Chabane_2022,
author = {Lydia Chabane and Alexandre Lazarescu and Gatien Verley},
title = {Effective Hamiltonians and Lagrangians for Conditioned Markov Processes at Large Volume},
journal = {J. Stat. Phys.},
publisher = {Springer Science and Business Media LLC},
year = {2022},
volume = {187},
number = {1},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Chabane_2022.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Chabane_2022.pdf},
doi = {https://doi.org/10.1007/s10955-022-02898-3}
}
|
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| Verley, G. | Dynamical equivalence classes for Markov jump processes | 2022 | J. Stat. Mech: Theory Exp. Vol. 2022(2), pp. 023211 |
article | DOI URL |
| Abstract: Two different Markov jump processes driven out of equilibrium by constant thermodynamic forces may have identical current fluctuations in the stationary state. The concept of dynamical equivalence classes emerges from this statement as proposed by Andrieux for discrete-time Markov chains on simple graphs. We define dynamical equivalence classes in the context of continuous-time Markov chains on multigraphs using the symmetric part of the rate matrices that define the dynamics. The freedom on the skew-symmetric part is at the core of the freedom inside a dynamical equivalence class. It arises from different splittings of the thermodynamic forces onto the system's transitions. | |||||
BibTeX:
@article{Verley2022vol2022,
author = {Gatien Verley},
title = {Dynamical equivalence classes for Markov jump processes},
journal = {J. Stat. Mech: Theory Exp.},
publisher = {IOP Publishing},
year = {2022},
volume = {2022},
number = {2},
pages = {023211},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2022vol2022.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2022vol2022.pdf},
doi = {https://doi.org/10.1088/1742-5468/ac4981}
}
|
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| Vroylandt, H., Esposito, M. and Verley, G. | Efficiency Fluctuations of Stochastic Machines Undergoing a Phase Transition | 2020 | Phys. Rev. Lett. Vol. 124(25) |
article | DOI URL |
| Abstract: We study the efficiency fluctuations of a stochastic heat engine made of N interacting unicyclic machines and undergoing a phase transition in the macroscopic limit. Depending on N and on the observation time, the machine can explore its whole phase space or not. This affects the engine efficiency that either strongly fluctuates on a large interval of equiprobable efficiencies (ergodic case) or fluctuates close to several most likely values (nonergodic case). We also provide a proof that despite the phase transition, the decay rate of the efficiency distribution at the reversible efficiency remains the largest one although other efficiencies can now decay equally fast. | |||||
BibTeX:
@article{Vroylandt2020vol124,
author = {Hadrien Vroylandt and Massimiliano Esposito and Gatien Verley},
title = {Efficiency Fluctuations of Stochastic Machines Undergoing a Phase Transition},
journal = {Phys. Rev. Lett.},
publisher = {American Physical Society (APS)},
year = {2020},
volume = {124},
number = {25},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2020vol124.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2020vol124.pdf},
doi = {https://doi.org/10.1103/physrevlett.124.250603}
}
|
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| Chabane, L., Chétrite, R. and Verley, G. | Periodically driven jump processes conditioned on large deviations | 2020 | J. Stat. Mech: Theory Exp. Vol. 2020(3), pp. 033208 |
article | DOI URL |
| Abstract: We study the fluctuations of systems modeled by time periodically driven Markov jump processes. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical biasing and Doob transform, we characterize the asymptotic fluctuations of such observables after a large number of periods by obtaining the Markov process that produces them. We show that this process, called driven process, is the optimizer under constraint of the large deviation function for occupation and jumps. | |||||
BibTeX:
@article{Chabane_2020,
author = {Lydia Chabane and Raphaël Chétrite and Gatien Verley},
title = {Periodically driven jump processes conditioned on large deviations},
journal = {J. Stat. Mech: Theory Exp.},
publisher = {IOP Publishing},
year = {2020},
volume = {2020},
number = {3},
pages = {033208},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Chabane_2020vol.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Chabane_2020vol.pdf},
doi = {https://doi.org/10.1088/1742-5468/ab74c4}
}
|
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| Vroylandt, H., Lacoste, D. and Verley, G. | An ordered set of power-efficiency trade-offs | 2019 | J. Stat. Mech: Theory Exp. Vol. 2019(5), pp. 054002 |
article | DOI URL |
| Abstract: In this paper, we derive a number of inequalities which express power-efficiency trade-offs that hold generally for thermodynamic machines operating in non-equilibrium stationary states. One of these inequalities concerns the output power, which is bounded by a quadratic function of the thermodynamic efficiency multiplied by a factor. Different factors can be obtained according to the level of knowledge one has about the underlying dynamics of the machine, they can depend for instance on the covariance of the input flux, the dynamical activity, or the non-equilibrium conductance. | |||||
BibTeX:
@article{Vroylandt2019_vol2019,
author = {Hadrien Vroylandt and David Lacoste and Gatien Verley},
title = {An ordered set of power-efficiency trade-offs},
journal = {J. Stat. Mech: Theory Exp.},
publisher = {IOP Publishing},
year = {2019},
volume = {2019},
number = {5},
pages = {054002},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2019_vol2019.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2019_vol2019.pdf},
doi = {https://doi.org/10.1088/1742-5468/ab14d7}
}
|
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| Vroylandt, H. and Verley, G. | Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity | 2018 | J. Stat. Phys. Vol. 174(2), pp. 404-432 |
article | DOI URL |
| Abstract: Dynamical ensembles have been introduced to study constrained stochastic processes. In the microcanonical ensemble, the value of a dynamical observable is constrained to a given value. In the canonical ensemble a bias is introduced in the process to move the mean value of this observable. The equivalence between the two ensembles means that calculations in one or the other ensemble lead to the same result. In this paper, we study the physical conditions associated with ensemble equivalence and the consequences of non-equivalence. For continuous time Markov jump processes, we show that ergodicity guarantees ensemble equivalence. For non-ergodic systems or systems with emergent ergodicity breaking, we adapt a method developed for equilibrium ensembles to compute asymptotic probabilities while caring about the initial condition. We illustrate our results on the infinite range Ising model by characterizing the fluctuations of magnetization and activity. We discuss the emergence of non-ergodicity by showing that the initial condition can only be forgotten after a time that scales exponentially with the number of spins. | |||||
BibTeX:
@article{Vroylandt2018_vol174,
author = {Vroylandt, Hadrien and Verley, Gatien},
title = {Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity},
journal = {J. Stat. Phys.},
year = {2018},
volume = {174},
number = {2},
pages = {404--432},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2018_Vol174.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2018_Vol174.pdf},
doi = {https://doi.org/10.1007/s10955-018-2186-7}
}
|
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| Vroylandt, H., Lacoste, D. and Verley, G. | Degree of coupling and efficiency of energy converters far-from-equilibrium | 2018 | J. Stat. Mech: Theory Exp. | article | DOI URL |
| Abstract: In this paper, we introduce a real symmetric and positive semi-definite matrix, which we call the non-equilibrium conductance matrix, and which generalizes the Onsager response matrix for a system in a non-equilibrium stationary state. We then express the thermodynamic efficiency in terms of the coefficients of this matrix using a parametrization similar to the one used near equilibrium. This framework, then valid arbitrarily far from equilibrium allows to set bounds on the thermodynamic efficiency by a universal function depending only on the degree of coupling between input and output currents. It also leads to new general power-efficiency trade-offs valid for macroscopic machines that are compared to trade-offs previously obtained from uncertainty relations. We illustrate our results on an unicycle heat to heat converter and on a discrete model of a molecular motor. | |||||
BibTeX:
@article{Vroylandt2018vol2018,
author = {Hadrien Vroylandt and David Lacoste and Gatien Verley},
title = {Degree of coupling and efficiency of energy converters far-from-equilibrium},
journal = {J. Stat. Mech: Theory Exp.},
year = {2018},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2018_vol2018.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2018_vol2018.pdf},
doi = {https://doi.org/10.1088/1742-5468/aaa8fe}
}
|
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| Vroylandt, H., Esposito, M. and Verley, G. | Collective effects enhancing power and efficiency | 2017 | Europhys. Lett. Vol. 120(3), pp. 30009 |
article | DOI URL |
| Abstract: Energy conversion is most efficient for micro or nano machines with tight coupling between input and output power. To reach meaningful amounts of power, ensembles of N such machines must be considered. We use a model system to demonstrate that interactions between N tightly coupled nanomachines can enhance the power output per machine. Furthermore, while interactions break tight coupling and thus lower efficiency in finite ensembles, the macroscopic limit restores it and enhances both the efficiency and the output power per nanomachine. |
|||||
BibTeX:
@article{Vroylandt2017_vol120,
author = {Hadrien Vroylandt and Massimiliano Esposito and Gatien Verley},
title = {Collective effects enhancing power and efficiency},
journal = {Europhys. Lett.},
publisher = {IOP Publishing},
year = {2017},
volume = {120},
number = {3},
pages = {30009},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2017_vol120.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2017_vol120.pdf},
doi = {https://doi.org/10.1209/0295-5075/120/30009}
}
|
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| Verley, G. | Nonequilibrium thermodynamic potentials for continuous-time Markov chains | 2016 | Phys. Rev. E Vol. 93, pp. 012111 |
article | DOI URL |
| Abstract: We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations. |
|||||
BibTeX:
@article{Verley2016_vol93,
author = {Verley, Gatien},
title = {Nonequilibrium thermodynamic potentials for continuous-time Markov chains},
journal = {Phys. Rev. E},
publisher = {American Physical Society},
year = {2016},
volume = {93},
pages = {012111},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2016_vol93.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2016_vol93.pdf},
doi = {https://doi.org/10.1103/PhysRevE.93.012111}
}
|
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| Vroylandt, H., Bonfils, A. and Verley, G. | Efficiency fluctuations of small machines with unknown losses | 2016 | Phys. Rev. E Vol. 93, pp. 052123 |
article | DOI URL |
| Abstract: The efficiency statistics of a small thermodynamic machine has been recently investigated assuming that the total dissipation is a linear combination of two currents: the input and output currents. Here, we relax this standard assumption and consider the question of the efficiency fluctuations for a machine involving three different currents, first in full generality and second for two different examples. Since the third current may not be measurable and/or may decrease the machine efficiency, our motivation is to study the effect of unknown losses in small machines. |
|||||
BibTeX:
@article{Vroylandt2016_vol93,
author = {Vroylandt, H. and Bonfils, A. and Verley, G.},
title = {Efficiency fluctuations of small machines with unknown losses},
journal = {Phys. Rev. E},
publisher = {American Physical Society},
year = {2016},
volume = {93},
pages = {052123},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2016_vol93.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Vroylandt2016_vol93.pdf},
doi = {https://doi.org/10.1103/PhysRevE.93.052123}
}
|
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| Polettini, M., Verley, G. and Esposito, M. | Efficiency Statistics at All Times: Carnot Limit at Finite Power | 2015 | Phys. Rev. Lett. Vol. 114, pp. 050601 |
article | DOI URL |
| Abstract: 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 ζ . 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 ζ → 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 / ζ microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches the Carnot limit at finite entropy production. |
|||||
BibTeX:
@article{Polettini2015_vol114,
author = {Polettini, M. and Verley, G. and Esposito, M.},
title = {Efficiency Statistics at All Times: Carnot Limit at Finite Power},
journal = {Phys. Rev. Lett.},
publisher = {American Physical Society},
year = {2015},
volume = {114},
pages = {050601},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Polettini2015_vol114.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Polettini2015_vol114.pdf},
doi = {https://doi.org/10.1103/PhysRevLett.114.050601}
}
|
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| Tusch, S., Kundu, A., Verley, G., Blondel, T., Miralles, V., Démoulin, D., Lacoste, D. and Baudry, J. | Energy versus Information Based Estimations of Dissipation Using a Pair of Magnetic Colloidal Particles | 2014 | Phys. Rev. Lett. Vol. 112, pp. 180604 |
article | DOI URL |
| Abstract: 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. |
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BibTeX:
@article{Tusch2014_vol112,
author = {Tusch, S. and Kundu, A. and Verley, G. and Blondel, T. and Miralles, V. and Démoulin, D. and Lacoste, D. and Baudry, J.},
title = {Energy versus Information Based Estimations of Dissipation Using a Pair of Magnetic Colloidal Particles},
journal = {Phys. Rev. Lett.},
publisher = {American Physical Society},
year = {2014},
volume = {112},
pages = {180604},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Tusch2014_vol112.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Tusch2014_vol112.pdf},
doi = {https://doi.org/10.1103/PhysRevLett.112.180604}
}
|
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| Verley, G., Van den Broeck, C. and Esposito, M. | Work statistics in stochastically driven systems | 2014 | New J. Phys. Vol. 16(9), pp. 095001 |
article | DOI URL |
| Abstract: 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. |
|||||
BibTeX:
@article{Verley2014_vol16,
author = {Verley, G. and Van den Broeck, C. and Esposito, M.},
title = {Work statistics in stochastically driven systems},
journal = {New J. Phys.},
year = {2014},
volume = {16},
number = {9},
pages = {095001},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2014_vol16.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2014_vol16.pdf},
doi = {https://doi.org/10.1088/1367-2630/16/9/095001}
}
|
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| Verley, G., Willaert, T., Van den Broeck, C. and Esposito, M. | The unlikely Carnot efficiency | 2014 | Nat. Commun. Vol. 5, pp. 4721 |
article | DOI URL |
| Abstract: 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. |
|||||
BibTeX:
@article{Verley2014_vol5,
author = {Verley, G. and Willaert, T. and Van den Broeck, C. and Esposito, M.},
title = {The unlikely Carnot efficiency},
journal = {Nat. Commun.},
year = {2014},
volume = {5},
pages = {4721},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2014_vol5_Arxiv.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2014_vol5_Arxiv.pdf},
doi = {https://doi.org/10.1038/ncomms5721}
}
|
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| Verley, G., Willaert, T., Van den Broeck, C. and Esposito, M. | Universal theory of efficiency fluctuations | 2014 | Phys. Rev. E Vol. 90, pp. 052145 |
article | DOI URL |
| Abstract: Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from equilibrium. In particular, the probabilities for observing the reversible efficiency and the least likely efficiency are identical to those of the same machine working under the time-reversed driving. For time-symmetric drivings, this reversible and the least probable efficiency coincide. |
|||||
BibTeX:
@article{Verley2014_vol90,
author = {Verley, G. and Willaert, T. and Van den Broeck, C. and Esposito, M.},
title = {Universal theory of efficiency fluctuations},
journal = {Phys. Rev. E},
publisher = {American Physical Society},
year = {2014},
volume = {90},
pages = {052145},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2014_vol90.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2014_vol90.pdf},
doi = {https://doi.org/10.1103/PhysRevE.90.052145}
}
|
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| Verley, G., Van den Broeck, C. and Esposito, M. | Modulated two-level system: Exact work statistics | 2013 | Phys. Rev. E Vol. 88, pp. 032137 |
article | DOI URL |
| Abstract: 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. |
|||||
BibTeX:
@article{Verley2013_vol88,
author = {Verley, G. and Van den Broeck, C. and Esposito, M.},
title = {Modulated two-level system: Exact work statistics},
journal = {Phys. Rev. E},
publisher = {American Physical Society},
year = {2013},
volume = {88},
pages = {032137},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2013_vol88.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2013_vol88.pdf},
doi = {https://doi.org/10.1103/PhysRevE.88.032137}
}
|
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| Verley, G. | Fluctuations et réponse des systèmes hors d'équillibre | 2012 | School: Université Pierre et Marie Curie | phdthesis | URL |
| Abstract: In recent years, a broad number of works have shed light on the nature of irreversibility of nonequilibrium phenomena, have permitted to redefine quantities such as work or entropy production at the level of trajectories, and to enlighten their symmetries through the fluctuation theorems. During this thesis, we focused on these results in a purely classical and Markovian framework. We have unified the various formulations of the generalized fluctuation dissipation theorem around steady and unsteady nonequilibrium state by identifying the various sources of irreversibility and by making them appear in the system response. We have tried to link the fluctuation theorems with the theory of linear response which was possible using a generalization of the relation of Hatano and Sasa. In doing so, we found that different functionals verified symmetry properties similar to the fluctuation theorem for total entropy production. The study of the generalization of Hatano and Sasa relation led us to an inequality of the same type as the Clausius inequality. This new inequality gives a lower bound for the system entropy production during transition between non-stationary states, as the Clausius inequality do for transitions between equilibrium states. We have illustrated these ideas on a few simple cases analytical or numerical and in an experiment where we manipulate magnetic colloids. In these experiments, a Crooks relation is expected for a system with space dependent diffusion coefficient, allowing to consider new tests of stochastic thermodynamics. |
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BibTeX:
@phdthesis{Verley2012_vol,
author = {Verley, G.},
title = {Fluctuations et réponse des systèmes hors d'équillibre},
school = {Université Pierre et Marie Curie},
year = {2012},
note = {http://tel.archives-ouvertes.fr/tel-00748590PDF},
url = {http://tel.archives-ouvertes.fr/tel-00748590}
}
|
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| Verley, G., Chétrite, R. and Lacoste, D. | Inequalities Generalizing the Second Law of Thermodynamics for Transitions between Non-stationary States | 2012 | Phys. Rev. Lett. Vol. 108, pp. 120601 |
article | DOI URL |
| Abstract: 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. |
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BibTeX:
@article{Verley2012_vol108,
author = {Verley, G. and Chétrite, R. and Lacoste, D.},
title = {Inequalities Generalizing the Second Law of Thermodynamics for Transitions between Non-stationary States},
journal = {Phys. Rev. Lett.},
publisher = {American Physical Society},
year = {2012},
volume = {108},
pages = {120601},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2012_vol108.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2012_vol108.pdf},
doi = {https://doi.org/10.1103/PhysRevLett.108.120601}
}
|
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| Verley, G. and Lacoste, D. | Fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium | 2012 | Phys. Rev. E Vol. 86, pp. 051127 |
article | DOI URL |
| Abstract: 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. |
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BibTeX:
@article{Verley2012_vol86a,
author = {Verley, G. and Lacoste, D.},
title = {Fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium},
journal = {Phys. Rev. E},
publisher = {American Physical Society},
year = {2012},
volume = {86},
pages = {051127},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2012_vol86a.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2012_vol86a.pdf},
doi = {https://doi.org/10.1103/PhysRevE.86.051127}
}
|
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| Verley, G. and Lacoste, D. | Fluctuations and response from a Hatano and Sasa approach | 2012 | Phys. Scr. Vol. 86, pp. 058505 |
article | DOI URL |
| Abstract: 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. |
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BibTeX:
@article{Verley2012_vol86,
author = {Verley, G. and Lacoste, D.},
title = {Fluctuations and response from a Hatano and Sasa approach},
journal = {Phys. Scr.},
year = {2012},
volume = {86},
pages = {058505},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2012_vol86.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2012_vol86.pdf},
doi = {https://doi.org/10.1088/0031-8949/86/05/058505}
}
|
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| Verley, G., Chétrite, R. and Lacoste, D. | Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain | 2011 | J. Stat. Mech: Theory Exp. Vol. 10, pp. P10025 |
article | DOI URL |
| Abstract: 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. |
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BibTeX:
@article{Verley2011_vol10,
author = {Verley, G. and Chétrite, R. and Lacoste, D.},
title = {Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain},
journal = {J. Stat. Mech: Theory Exp.},
year = {2011},
volume = {10},
pages = {P10025},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2011_vol10.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2011_vol10.pdf},
doi = {https://doi.org/10.1088/1742-5468/2011/10/P10025}
}
|
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| Verley, G. and Lacoste, D. | Fluctuation relations and fluctuation-response for molecular motors | 2011 | Vol. 1332AIP Conf. Proc., pp. 247-248 |
inproceedings | DOI URL |
| Abstract: 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. |
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BibTeX:
@inproceedings{Verley2011_vol1332,
author = {Verley, G. and Lacoste, D.},
title = {Fluctuation relations and fluctuation-response for molecular motors},
booktitle = {AIP Conf. Proc.},
year = {2011},
volume = {1332},
pages = {247--248},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2011_vol1332.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2011_vol1332.pdf},
doi = {https://doi.org/10.1063/1.3569518}
}
|
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| Verley, G., Mallick, K. and Lacoste, D. | Modified fluctuation-dissipation theorem for non-equilibrium steady states and applications to molecular motors | 2011 | Europhys. Lett. Vol. 93, pp. 10002 |
article | DOI URL |
| Abstract: 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. |
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BibTeX:
@article{Verley2011_vol93,
author = {Verley, G. and Mallick, K. and Lacoste, D.},
title = {Modified fluctuation-dissipation theorem for non-equilibrium steady states and applications to molecular motors},
journal = {Europhys. Lett.},
year = {2011},
volume = {93},
pages = {10002},
note = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2011_vol93.pdfPDF},
url = {https://pperso.ijclab.in2p3.fr/page_perso/Verley/Papers/Verley2011_vol93.pdf},
doi = {https://doi.org/10.1209/0295-5075/93/10002}
}
|
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