Numerical Test of Far-From-Equilibrium Fluctuation-Dissipation Identities

We test numerically a recently reported far-from-equilibrium

generalization of the fluctuation-dissipation relation that was

derived from a field theory [1]. The system we consider is classical

particles on a lattice undergoing diffusive hops and local chemical

reactions, and driven out of equilibrium by a time-varying local

potential. The hopping and reaction processes are simulated by

Anderson's modified next reaction method [2], which is a

Gillespie-type algorithm designed to handle time-dependent rates. For

small systems we are able to verify the Jarzynski and Crooks

relations, as well as a host of related nonequilibrium work

identities, thus demonstrating that this numerical method is capable

of adequately sampling the distribution of trajectories. Preliminary

numerical tests of the nonequilibrium fluctuation-dissipation relation

support its validity for a range of driving speeds.

[1] B.P. Vollmayr-Lee and J. Pham, Bull. Am. Phys. Soc., M55.2 (2024).

[2] D.F. Anderson, J. Chem. Phys. 127, 214107 (2007).