Effective temperature in steady-state dynamics from holography

Abstract

We argue that, within the realm of gauge-gravity duality, for a large class of systems in a steady-state there exists an effective thermodynamic description. This description comes equipped with an effective temperature and a free energy, but no well-defined notion of entropy. Such systems are described by probe degrees of freedom propagating in a much larger background, e.g. N f number of $$ \mathcal{N}=2 $$ hypermultiplets in $$ \mathcal{N}=4 $$ SU(N c ) super Yang-Mills theory, in the limit N f ≪ N c . The steady-state is induced by exciting an external electric field that couples to the hypermultiplets and drives a constant current. With various stringy examples, we demonstrate that an open string equivalence principle determines an unique effective temperature for all fluctuations in the probe-sector. We further discuss various properties of the corresponding open string metric that determines the effective geometry which the probe degrees of freedom are coupled to. We also comment on the non-Abelian generalization, where the effective temperature depends on the corresponding sector of the fluctuation modes.