## A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics (1999)

Venue: | J. STAT. PHYS |

Citations: | 52 - 2 self |

### BibTeX

@ARTICLE{Lebowitz99agallavotti-cohen,

author = {Joel L. Lebowitz and Herbert Spohn},

title = {A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics},

journal = {J. STAT. PHYS},

year = {1999},

volume = {95},

pages = {333--365}

}

### Years of Citing Articles

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### Abstract

### Citations

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Citation Context ...ms to the deterministic evolution equations describing the isolated system [1]–[7]. Fully deterministic evolutions of systems coupled to infinitely extended reservoirs have also been investigated [8]–=-=[10]-=-, as have fully stochastic models [11]–[14]. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics [15, 16, 17]. In this scheme the SNS is ... |

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Citation Context ...en so that the system evolves on a compact surface (generally one of constant energy) in phase space. The resulting dynamics no longer conserves phase space volume, which is contracted on the average =-=[19]-=-. Consequently, the SNS is singular with respect to the Liouville (volume) measure induced on the surface. While the jury is still out on what has or can be achieved by such a dynamical systems approa... |

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Citation Context ...eat flux from the higher to the lower temperature reservoir. (This is a variation of the model used to describe heat flow in a crystal where the Langevin forces act on the particles in the end layers =-=[3]-=-, [10]). We now follow the method explained in Section 6. For the similarity transformation we use exp [ − N∑ { β(qj) j=1 1 2m p2j + Vw(qj) + 1 2 N∑ }] V (qi − qj) . (7.2) The local inverse temperatur... |

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Citation Context ... terms to the deterministic evolution equations describing the isolated system [1]–[7]. Fully deterministic evolutions of systems coupled to infinitely extended reservoirs have also been investigated =-=[8]-=-–[10], as have fully stochastic models [11]–[14]. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics [15, 16, 17]. In this scheme the SN... |

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Citation Context ...tions describing the isolated system [1]–[7]. Fully deterministic evolutions of systems coupled to infinitely extended reservoirs have also been investigated [8]–[10], as have fully stochastic models =-=[11]-=-–[14]. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics [15, 16, 17]. In this scheme the SNS is maintained by deterministic external d... |

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Citation Context ...irs have also been investigated [8]–[10], as have fully stochastic models [11]–[14]. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics =-=[15, 16, 17]-=-. In this scheme the SNS is maintained by deterministic external driving forces which are balanced by a “friction term” suitably chosen so that the system evolves on a compact surface (generally one o... |

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Citation Context ...irs have also been investigated [8]–[10], as have fully stochastic models [11]–[14]. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics =-=[15, 16, 17]-=-. In this scheme the SNS is maintained by deterministic external driving forces which are balanced by a “friction term” suitably chosen so that the system evolves on a compact surface (generally one o... |

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Citation Context ...lume) measure induced on the surface. While the jury is still out on what has or can be achieved by such a dynamical systems approach, there are some intriguing theoretical results which have emerged =-=[20, 21]-=-. In particular Gallavotti and Cohen [22] motivated by results of computer simulations [23] discovered that under suitable assumptions these SNS satisfy a certain symmetry, which they doobed a “fluctu... |

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Citation Context ...istory. The interactions of the system with the reservoirs are usually modeled by the addition of stochastic boundary terms to the deterministic evolution equations describing the isolated system [1]–=-=[7]-=-. Fully deterministic evolutions of systems coupled to infinitely extended reservoirs have also been investigated [8]–[10], as have fully stochastic models [11]–[14]. A more recent development has bee... |

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Citation Context ... Since the noise vanishes on large parts of the phase space, even the convergence to the steady state is not obvious. To our knowledge there are only a few rigorous investigations of SNS of this type =-=[3, 4, 5, 7, 10]-=-. In [5, 7] classical point particles are considered. At a collision with the wall they are reflected with a Maxwellian distribution at the local temperature of the wall. Existence and uniqueness of t... |

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Citation Context ...ng history. The interactions of the system with the reservoirs are usually modeled by the addition of stochastic boundary terms to the deterministic evolution equations describing the isolated system =-=[1]-=-–[7]. Fully deterministic evolutions of systems coupled to infinitely extended reservoirs have also been investigated [8]–[10], as have fully stochastic models [11]–[14]. A more recent development has... |

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Citation Context ... Since the noise vanishes on large parts of the phase space, even the convergence to the steady state is not obvious. To our knowledge there are only a few rigorous investigations of SNS of this type =-=[3, 4, 5, 7, 10]-=-. In [5, 7] classical point particles are considered. At a collision with the wall they are reflected with a Maxwellian distribution at the local temperature of the wall. Existence and uniqueness of t... |

1 |
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Citation Context ... describing the isolated system [1]–[7]. Fully deterministic evolutions of systems coupled to infinitely extended reservoirs have also been investigated [8]–[10], as have fully stochastic models [11]–=-=[14]-=-. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics [15, 16, 17]. In this scheme the SNS is maintained by deterministic external drivin... |

1 |
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Citation Context ...irs have also been investigated [8]–[10], as have fully stochastic models [11]–[14]. A more recent development has been the study of SNS of systems evolving via deterministic “thermostatted” dynamics =-=[15, 16, 17]-=-. In this scheme the SNS is maintained by deterministic external driving forces which are balanced by a “friction term” suitably chosen so that the system evolves on a compact surface (generally one o... |

1 |
New theoretical ideas in nonequilibrum statistical mechanics
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Citation Context ...lume) measure induced on the surface. While the jury is still out on what has or can be achieved by such a dynamical systems approach, there are some intriguing theoretical results which have emerged =-=[20, 21]-=-. In particular Gallavotti and Cohen [22] motivated by results of computer simulations [23] discovered that under suitable assumptions these SNS satisfy a certain symmetry, which they doobed a “fluctu... |

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