Entropic aging and extreme value statistics

Abstract

Entropic aging consists in a progressive slowing down of the low-temperature dynamics of a glassy system due to the rarefaction of downwards directions on the energy landscape, as lower and lower energy levels are reached. A prototypical model exhibiting this scenario is the Barrat-Mézard model. We argue that in the zero-temperature limit, this model precisely corresponds to a dynamical realization of extreme value statistics, providing an interesting connection between the two fields. This mapping directly yields the long-time asymptotic shape of the dynamical energy distribution, which is then one of the standard extreme value distributions (Gumbel, Weibull or Fréchet), thus restricting the class of asymptotic energy distributions with respect to the original preasymptotic results. We also briefly discuss similarities and differences between the Barrat-Mézard model and undriven dissipative systems like granular gases.

8 pages, to appear in J. Phys. A

References in corpus (16)

• Models of traps and glass phenomenology
• Universality Classes for Extreme Value Statistics
• 1/f Noise and Extreme Value Statistics
• Glassiness in a model without energy barriers
• Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system
• Generalised extreme value statistics and sum of correlated variables
• Global fluctuations and Gumbel statistics
• Records in a changing world
• Phase space diffusion and low temperature aging
• The longest excursion of stochastic processes in nonequilibrium systems
• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
• Intermittency, aging and record fluctuations
• Scaling and universality of critical fluctuations in granular gases
• Relaxation processes and entropic traps in the Backgammon model
• Crossover from entropic to thermal dynamics in glassy models
• Mesoscopic Theory of Critical Fluctuations in Isolated Granular Gases

Cited by in corpus (4)

• Discrete Sampling of Extreme Events Modifies Their Statistics
• Effective Trap-like Activated Dynamics in a Continuous Landscape
• Aging of the frictional properties induced by temperature variations
• Competition between Barrier- and Entropy-Driven Activation in Glasses