Nonequilibrium fluctuation-dissipation relation from holography

Abstract

We derive a nonequilibrium fluctuation-dissipation relation for bosonic correlation functions from holography in the classical gravity approximation at strong coupling. This generalizes the familiar thermal fluctuation-dissipation relation in the absence of external sources. This also holds universally for any nonequilibrium state which can be obtained from a stable thermal equilibrium state in perturbative derivative (hydrodynamic) and amplitude (nonhydrodynamic) expansions. Therefore, this can provide a strong experimental test for the applicability of the holographic framework. We discuss how it can be tested in heavy-ion collisions. We also make a conjecture regarding multipoint holographic nonequilibrium Green's functions.

Thermalization of the spectral function in strongly coupled two dimensional conformal field theories

“…A complementary approach to the holographic non-equilibrium spectral function and the fluctuation-dissipation relation has been developed in [27,28]. They consider perturbative expansions (derivative and amplitude) away from thermal equilibrium, working first at leading order [27] (where they also study non-equilibrium shift effects) and then extending to higher orders [28].…”

Holographic isotropization linearized

“…A systematic discussion of the amplitude expansion of Einstein's equations in the more general homogeneous but non-diagonal situation can be found in [26].…”

Gravitational collapse of thin shells: time evolution of the holographic entanglement entropy

“…At the same time, technical leaps have been taken in the incorporation of inhomogeneities and anisotropies in thermalization dynamics [24][25][26][27][28], the development of a formalism to evaluate out-of-equilibrium Green's functions [29][30][31][32], as well as the first studies of thermalization dynamics away from the infinite coupling limit [33][34][35][36] and in non-conformal backgrounds [37].…”