Christian Maes: Fluctuation-response relations out-of-equilibrium


Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the frenesy, the linear order of excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle. The response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics.

Collaborations with Marco Baiesi, Eliran Boksenbojm and Bram Wynants.

M. Baiesi, C. Maes and B. Wynants: Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions, J.Stat.Phys. 137, 1094 (2009).
Christian Maes and Bram Wynants: On a response formula and its interpretation, arXiv:0910.2320.
M. Baiesi, E. Boksenbojm, C. Maes and B. Wynants: Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics. arXiv:0912.0694.
M. Baiesi, C. Maes and B. Wynants: Fluctuations and response of nonequilibrium states, Phys. Rev. Lett. 103, 010602 (2009).