Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 54: Statistical Physics: General II

DY 54.8: Talk

Thursday, March 12, 2026, 17:00–17:15, ZEU/0114

Derivation of a multi-dimensional non-equilibrium generalized Langevin equation — •Benjamin Hery — Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany

The Mori-Zwanzig formalism is a powerful theoretical framework for deriving generalized Langevin equations (GLEs) for observables of interest using evolution and projection operators. Using a multi-dimensional Mori projection operator, we derive a non-equilibrium Mori GLE for a multi-dimensional observable of interest A^→ that consists in a Markovian force, a running integral over time of a non-Markovian friction force, and a orthogonal force that is often interpreted as a random force. We study the structure of the derived GLE in three limiting cases: when the components of A^→ are uncorrelated, when the system is at equilibrium, and when both conditions happen at the same time. In particular, we highlight the presence of a contribution to the Markovian force that takes the form of an instantaneous friction force which only vanishes when the components of A^→ are uncorrelated.

Keywords: Mori-Zwanzig formalism; generalized Langevin equation; time-dependent Hamiltonian; non-equilibrium physics; multi-dimensional observable