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).