A fluctuation theorem in a random environment

Bonetto, Federico; Gallavotti, Giovanni; Gentile, Guido

doi:10.1017/s0143385707000417

Cited by 11 publications

(12 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore it admits a SRB distribution which can also be studied very explicitly by perturbation theory, [84,30]Ga996bBGG007, [103, Sec. 10.4]GBG004.…”

Section: Local Fluctuations: An Examplementioning

confidence: 99%

See 1 more Smart Citation

Nonequilibrium and Irreversibility

Gallavotti

2014

Theoretical and Mathematical Physics

View full text Add to dashboard Cite

“…Therefore it admits a SRB distribution which can also be studied very explicitly by perturbation theory, [84,30]Ga996bBGG007, [103, Sec. 10.4]GBG004.…”

Section: Local Fluctuations: An Examplementioning

confidence: 99%

“…30 The above equation can also be written for the components y, z, and of course we shall suppose that the motions in the different directions behave in the same way and that, for each group of points, the quantity δ log i assumes the same value for the three coordinates.…”

Section: Clausius' Mechanical Proof Of the Heat Theoremmentioning

confidence: 99%

Nonequilibrium and Irreversibility

Gallavotti

2014

Theoretical and Mathematical Physics

View full text Add to dashboard Cite

“…(d) chaotic motions may occur under influence of stochastic perturbations, so that extensions of FT to stochastic systems may need to be considered. This is not really a problem because a random perturbation can be imagined as generated by coupling of the system to another dynamical system (which, for instance, in simulations would be the random number generator from which the noise is drawn), nevertheless it demands careful analysis, [65]. (e) Nonconvex shape of ζ(p), at |p − 1| beyond the root mean square deviation, see Fig.3, is seen often, possibly always, in the experiments that have been attempted to study large deviations.…”

Section: Experiments ?mentioning

confidence: 99%

Heat and fluctuations from order to chaos

Gallavotti

2008

Eur. Phys. J. B

Self Cite

View full text Add to dashboard Cite

The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e.existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as 10 23 degrees of freedom systems, i.e. for simple as well as very complex systems, and reflecting the Hamiltonian nature of the microscopic motion. In Nonequilibrium Thermodynamics theorems of comparable generality do not seem to be available. Yet it is possible to find general, model independent, properties valid even for simple chaotic systems (i.e. the hyperbolic ones), which acquire special interest for large systems: the Chaotic Hypothesis leads to the Fluctuation Theorem which provides general properties of certain very large fluctuations and reflects the time-reversal symmetry. Implications on Fluids and Quantum systems are briefly hinted. The physical meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation Theorem is discussed in the context of their interpretation and relevance in terms of Coarse Grained Partitions of phase space. This review is written taking some care that each section and appendix is readable either independently of the rest or with only few cross references. * Review

show abstract

“…Such an extension of the scope of fluctuation relations is a possibility in the stationary case as well, but it becomes a necessity in many transient situations. Within the theory of the hyperbolic dynamical systems, the stationary fluctuation theorem of [35] was recently generalized to the random dynamics in [8].…”

Section: Introductionmentioning

confidence: 99%

Fluctuation Relations for Diffusion Processes

Chétrite

Gawędzki

2008

Commun. Math. Phys.

153

349

View full text Add to dashboard Cite

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.

show abstract

A fluctuation theorem in a random environment

Abstract: A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.

Cited by 11 publications

References 16 publications

Nonequilibrium and Irreversibility

Nonequilibrium and Irreversibility

Heat and fluctuations from order to chaos

Fluctuation Relations for Diffusion Processes

Contact Info

Product

Resources

About