Journal of Statistical Physics

, Volume 154, Issue 3, pp 705–722 | Cite as

On the Second Fluctuation–Dissipation Theorem for Nonequilibrium Baths

  • Christian Maes


Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation–dissipation theorem. We show what is the proper nonequilibrium extension, to be applied when the environment is itself active and driven. In particular we determine the effective Langevin dynamics of a probe from integrating out a steady nonequilibrium environment. The friction kernel picks up a frenetic contribution, i.e., involving the environment’s dynamical activity, responsible for the breaking of the standard Einstein relation.


Active medium Fluctuation–dissipation theorem Nonequilibrium reduced dynamics 



We thank Marco Baiesi and Urna Basu for helpful discussions.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Instituut voor Theoretische FysicaKU LeuvenLouvainBelgium

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