Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics

Cugliandolo, Leticia F.; Kurchan, Jorge; Peliti, Luca

doi:10.1103/physreve.55.3898

Cited by 805 publications

(1,327 citation statements)

References 64 publications

Supporting

Mentioning

1,256

Contrasting

Unclassified

Order By: Relevance

“…It has become customary [13,14,15,16] to characterize departure from equilibrium by the fluctuation-dissipation ratio X(t, s) = T R(t, s) ∂C(t, s) ∂s…”

Section: Fluctuation-dissipation Theorem: Equilibrium Vs Nonequilibrmentioning

confidence: 99%

See 1 more Smart Citation

Nonequilibrium dynamics of urn models

Godrèche

Luck

2002

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Abstract. Dynamical urn models, such as the Ehrenfest model, have played an important role in the early days of statistical mechanics. Dynamical manyurn models generalize the former models in two respects: the number of urns is macroscopic, and thermal effects are included. These many-urn models are exactly solvable in the mean-field geometry. They allow analytical investigations of the characteristic features of nonequilibrium dynamics referred to as aging, including the scaling of correlation and response functions in the two-time plane and the violation of the fluctuation-dissipation theorem. This review paper contains a general presentation of these models, as well as a more detailed description of two dynamical urn models, the backgammon model and the zeta urn model. PrologueUrns containing balls, just as dice or playing cards, are ubiquitous in writings on probability theory, reminding us that this branch of mathematics owes its early developments to practical questions arising in playing games. Dynamical urn models, such as the Ehrenfest model, have played an important role in the elucidation of conceptual problems in statistical mechanics. More recently, dynamical many-urn models have been investigated in the mean-field geometry. These exactly solvable models exhibit characteristic features of nonequilibrium dynamics referred to as aging, such as the scaling of the correlation and response functions in the two-time plane and the violation of the fluctuation-dissipation theorem. This paper contains a didactic introduction to urn models (Section 1), a presentation of static and dynamical properties of many-urn models (Section 2), a reminder of the main characteristic features of aging (Section 3), and an overview of recent results on two dynamical urn models, namely the backgammon model (Section 4) and the zeta urn model (Section 5).

show abstract

“…It has become customary [13,14,15,16] to characterize departure from equilibrium by the fluctuation-dissipation ratio X(t, s) = T R(t, s) ∂C(t, s) ∂s…”

Section: Fluctuation-dissipation Theorem: Equilibrium Vs Nonequilibrmentioning

confidence: 99%

“…It often exhibits a non-trivial scaling behavior in the two-time plane, which is viewed as one of the salient features of aging. The definition (3.4) can be rephrased in terms of an effective temperature [14]:…”

Section: Fluctuation-dissipation Theorem: Equilibrium Vs Nonequilibrmentioning

confidence: 99%

Nonequilibrium dynamics of urn models

Godrèche

Luck

2002

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…The dependence of X on C would reflect the level of thermalization within different timescales. 15 The integrated form of the FD relation would become…”

Section: Generalized Fluctuation Dissipation Relationmentioning

confidence: 99%

Experimental investigation of the fluctuation dissipation relation in a spin glass

Hérisson

Ocio

2003

SPIE Proceedings

View full text Add to dashboard Cite

We present the first experimental determination of the time auto-correlation of magnetization in the nonstationary regime of a spin glass, and its quantitative comparison with the corresponding response, the magnetic relaxation function. These measurements were performed in a new experimental setup working as an absolute thermometer. Clearly, we observe a non-linear fluctuation-dissipation relation between correlation and relaxation, i.e. an effective temperature higher than the bath temperature in the aging regime. According to theoretical developments on mean field models, and lately on short range ones, in the limit of very large waiting times, the relation between relaxation and correlation in the aging regime becomes temperature independent for a given system. A scaling procedure allows us to extrapolate to the limit of long waiting times by separating stationary and non-stationary regimes and to check the validity of the temperature independence of the fluctuation dissipation relation in the non-stationary regime.

show abstract

“…II A. In particular, in this context, we are naturally led to consider FDRs, which turned out to be particularly useful in understanding various instances and features of the non-equilibrium dynamics of classical and quantum glassy systems [12][13][14].…”

Section: B Dynamic Correlations and Response Functionsmentioning

confidence: 99%

“…Our aim is to revisit here the problem of thermalization in isolated many-body quantum systems with tools developed for the study of the non-equilibrium behavior of classical glassy systems [12][13][14]. Our study builds upon a large number of papers published in recent years.…”

mentioning

confidence: 99%

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

View full text Add to dashboard Cite

Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Contents

show abstract

Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics

Cited by 805 publications

References 64 publications

Nonequilibrium dynamics of urn models

Nonequilibrium dynamics of urn models

Experimental investigation of the fluctuation dissipation relation in a spin glass

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Contact Info

Product

Resources

About