Free energy, stability, and particle source in dynamical holography

TL;DR

This paper explores the connection between thermodynamical and dynamical stability in holographic systems using conserved currents, introducing a generalized free energy and analyzing superfluid dynamics with particle sources.

Contribution

It establishes a formal relation between thermodynamical and dynamical stability in holography and extends the analysis beyond the probe limit.

Findings

Generalized free energy decreases monotonically during dynamic processes.

Thermodynamical stability implies dynamical stability.

Dynamical stability implies thermodynamical (meta-)stability.

Abstract

By using the conserved currents in the bulk space-time, we study dynamical holographic systems and the relation between thermodynamical and dynamical stability of such systems. In particular, in the probe limit a generalized free energy is defined with the property of monotonic decreasing in dynamic processes. It is then shown that the (absolute) thermodynamical stability implies the dynamical stability, while the linear dynamical stability implies the thermodynamical (meta-)stability. The holographic superfluid is taken as an example to illustrate our general formalism, where the dynamic evolution of the system in contact with a particle source is clarified by theoretical investigation and numerical verification. The case going beyond the probe limit is also discussed.