scholarly journals Mathematical foundation of nonequilibrium fluctuation–dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients

2020 ◽  
Vol 130 (1) ◽  
pp. 171-202
Author(s):  
Xian Chen ◽  
Chen Jia
Keyword(s):  
Diffusion Processes ◽  
Mathematical Foundation ◽  
Unbounded Coefficients ◽  
Fluctuation Dissipation ◽  
Inhomogeneous Diffusion ◽  
Nonequilibrium Fluctuation

scholarly journals On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 818
Author(s):  
Virginia Giorno ◽  
Amelia G. Nobile
Keyword(s):  
Probability Density ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Transition Probability ◽  
Passage Time ◽  
Probability Density Functions ◽  
Periodic Functions ◽  
Initial State ◽  
Transition Probability Density ◽  
Inhomogeneous Diffusion

General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial state. Many diffusion processes with time-dependent infinitesimal drift and infinitesimal variance are included in the considered class. For these processes, the transition probability density function is explicitly determined. Moreover, simulation procedures are applied to the diffusion processes obtained starting from Wiener and Ornstein–Uhlenbeck processes. Specific examples in which the infinitesimal moments include periodic functions are discussed.

scholarly journals A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

2017 ◽  
Vol 114 (8) ◽  
pp. 1838-1843 ◽  
Author(s):  
Marco Baity-Jesi ◽  
Enrico Calore ◽  
Andres Cruz ◽  
Luis Antonio Fernandez ◽  
José Miguel Gil-Narvión ◽  
...  
Keyword(s):  
Spin Glass ◽  
Glass Phase ◽  
Large Scale ◽  
Infinite Systems ◽  
Spin Glass Phase ◽  
Ising Spin ◽  
Fluctuation Dissipation ◽  
Equilibrium Probability ◽  
Large Scale Simulations ◽  
Nonequilibrium Fluctuation

We have performed a very accurate computation of the nonequilibrium fluctuation–dissipation ratio for the 3D Edwards–Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.

Sign in / Sign up

Export Citation Format

Share Document