Editing Fluctuation–dissipation theorem (section)

==Nonequilibrium driven systems==
In systems subjected to an external driving force, which could be an electromagnetic field or a mechanical shear flow, the standard fluctuation-dissipation theorem gets modified because the statistics of the bath is influenced by the driving field. As a result, the thermal noise becomes biased and the fluctuation-dissipation relation becomes intrinsically non-Markovian, typically with a memory related to the time-autocorrelation of the external field (for the case of a time-dependent external drive). These modified fluctuation-dissipation relations can be derived from a Caldeira-Leggett Hamiltonian for a particle interacting with a thermal bath, where both the particle and the bath respond to the external field.<ref>{{cite journal | title=Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields |doi=10.1103/PhysRevE.97.060102 | volume=97 |year=2018 |journal=Physical Review E |pages=060102(R) |author=Cui B.|author2= Zaccone A.|issue= |pmid= |arxiv=1802.09848 |bibcode= |s2cid= }}</ref><ref>{{cite journal | title=Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian |doi=10.1103/PhysRevE.107.064102| volume=107 |year=2023 |journal=Physical Review E |pages=064102 |author=Pelargonio S.|author2= Zaccone A.|issue= |pmid= |arxiv=2302.03982 |bibcode= |s2cid= }}</ref>