We present a fluctuation-response relation for arbitrary Markov
processes, relating the time correlation of a variable with its linear response to a external perturbation [Prost, Joanny, Parrondo,
Phys. Rev. Lett. 103, 090601 (2009)]. This relation allows us to apply
to general systems the strategy that non equilibrium statistical
mechanics developed to study the response of a physical system
close to equilibrium: Langevin equations, fluctuating linear
irreversible thermodynamic, etc. More precisely, we will give
some hints on how to build a reduced linear model that reproduces
such relation, providing a general tool to reduce the number of
variables and complexity of a system under weak external
perturbations.
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