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DY: Fachverband Dynamik und Statistische Physik

DY 6: Statistical Physics far from Thermal Equilibrium I

DY 6.4: Talk

Monday, March 18, 2024, 10:30–10:45, BH-N 334

Non-equilibrium generalized Langevin equation from a generic time-dependent Hamiltonian — •Benjamin Héry and Roland R. Netz — Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Department of Physics

It has become standard practice to describe non-equilibrium phenomena by heuristic Langevin equations with colored noise and time-dependent friction kernels that do not obey the fluctuation-dissipation theorem. Since these models are not derived from first-principle Hamiltonian dynamics, it is not clear whether they correspond to physically realizable scenarios. By exact Mori projection in phase space, we derive the non-equilibrium generalized Langevin equation (GLE) from a generic many-body Hamiltonian with a time-dependent force h(t) acting on an arbitrary phase-space dependent observable. The GLE is obtained in explicit form to all orders in h(t). We show that if the observable that is described by the GLE is Gaussian and related to the time-dependent Hamiltonian perturbation term, the resultant non-equilibrium GLE has the same form as the equilibrium GLE and obeys a fluctuation-dissipation theorem. This means that the extraction and simulation methods developed for equilibrium GLEs can be used also for non-equilibrium Gaussian variables. This is a non-trivial and very useful result, as many observables that characterize non-equilibrium systems display Gaussian statistics.

Keywords: non-equilibrium systems; generalized Langevin equations; Hamiltonian dynamics; projection formalism