Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
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Vroylandt, H., Esposito, M. and Verley, G. | Collective effects enhancing power and efficiency | 2018 | Europhys. Lett. Vol. 120, 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 (N → ∞) restores it and enhances both the efficiency and the output power per nanomachine. |
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BibTeX:
@article{Vroylandt2018_vol120, author = {Vroylandt, H. and Esposito, M. and Verley, G.}, title = {Collective effects enhancing power and efficiency}, journal = {Europhys. Lett.}, year = {2018}, volume = {120}, pages = {30009}, url = {http://pperso.th.u-psud.fr/page_perso/Verley/Papers/Vroylandt2018_vol120.pdf}, doi = {https://doi.org/10.1209/0295-5075/120/30009} } |
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Vroylandt, H., Lacoste, D. and Verley, G. | Degree of coupling and efficiency of energy converters far-from-equilibrium | 2018 | Journal of Statistical Mechanics: Theory and Experiment Vol. 2018(2), pp. 023205 |
article | 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. |
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BibTeX:
@article{Vroylandt2018_vol2018, author = {Hadrien Vroylandt and David Lacoste and Gatien Verley}, title = {Degree of coupling and efficiency of energy converters far-from-equilibrium}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, year = {2018}, volume = {2018}, number = {2}, pages = {023205}, url = {http://pperso.th.u-psud.fr/page_perso/Verley/Papers/Vroylandt2018_vol2018.pdf} } |
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Vroylandt, H. and Verley, G. | Non equivalence of dynamical ensembles and emergent non ergodicity | 2018 | ArXiv e-prints | article | 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 thecanonical 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. |
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BibTeX:
@article{Vroylandt2018_volb, author = {Vroylandt, H. and Verley, G.}, title = {Non equivalence of dynamical ensembles and emergent non ergodicity}, journal = {ArXiv e-prints}, year = {2018}, url = {http://pperso.th.u-psud.fr/page_perso/Verley/Papers/Vroylandt2018_volb.pdf} } |
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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. |
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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}, url = {http://pperso.th.u-psud.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. |
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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}, url = {http://pperso.th.u-psud.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. |
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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}, url = {http://pperso.th.u-psud.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}, url = {http://pperso.th.u-psud.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. |
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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}, url = {http://pperso.th.u-psud.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(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. |
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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}, number = {4721}, url = {http://pperso.th.u-psud.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. |
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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}, url = {http://pperso.th.u-psud.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. |
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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}, url = {http://pperso.th.u-psud.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}, 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}, url = {http://pperso.th.u-psud.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}, url = {http://pperso.th.u-psud.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}, url = {http://pperso.th.u-psud.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. 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.}, year = {2011}, volume = {10}, pages = {P10025}, url = {http://pperso.th.u-psud.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 Conference Proceedings, 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 Conference Proceedings}, year = {2011}, volume = {1332}, pages = {247--248}, url = {http://pperso.th.u-psud.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}, url = {http://pperso.th.u-psud.fr/page_perso/Verley/Papers/Verley2011_vol93.pdf}, doi = {https://doi.org/10.1209/0295-5075/93/10002} } |