98-275 David Ruelle
General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem. (17K, Plain TeX) Apr 18, 98
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Abstract. Given a nonequilibrium steady state $\rho$ we derive formally the linear response formula $\delta_t\rho(\Phi)=\int_{-\infty}^t d\tau\rho(\delta_\tau F\cdot\nabla(\Phi\circ f^{t-\tau}))$ for the variation of the expectation value of $\Phi$ at time $t$ under an infinitesimal perturbation $\delta_\tau F$ of the acting forces. This leads to a form of the fluctuation-dissipation theorem valid far from equilibrium: the complex singularities of the susceptibility are in part those of the spectral density, and in part of a different nature to be discussed.

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