Fluctuations and Response of Nonequilibrium States

A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first order. The result gives a correction to the equilibrium fluctuation-dissipation theorem, in terms of the correlation between observable and excess in dynamical activity caused by the perturbation. Previous approaches to this problem are recovered and extended in a unifying scheme.

Figure 1

(a) Plots of $\chi (t)/\beta$ vs $[C(t)+D(t)]/2$ for times $t=5,10,\dots ,50$ (other parameters: see legend and $h=-0.1$, $d_1-d_n=0.8$). (b) $C(t=50)$ and $D(t=50)$ as functions of the unbalance between reservoir densities, for $\beta =1$, $n=20$. At equilibrium ($d_1=d_n$) one has $C(50)=D(50)$ as expected, while the difference between $C(50)$ and $D(50)$ is not negligible for strong nonequilibrium.