Computational complexity in analogue gravity

Abstract

Analogue gravity helps to find some gravitational systems which are similar to the evolution of perturbation in condensed matter systems. These analogies provide a very good tool for either side. In other words, some aspects of gravity could be simulated in condensed matter laboratories. In this study, we find an interpretation for computational complexity in condensed matter systems in terms of the flux density of the fluid and the analogue of the uncertainty principle as the Lloyd bound. We show that the Lloyd bound is reduced to the shear viscosity to entropy ratio (SVER). It has been revealed that the analogue gravity is a fluid located at a time-like finite cut-off surface (call it the bulk fluid) and we found the relation between SVER of the analogue gravity and the boundary fluid. Then we see that whenever the Kovtun–Son–Starinet (KSS) bound is satisfied in the boundary fluid, the KSS bound could be either satisfied in the bulk fluid or not; in addition, when the KSS bound is violated in the boundary fluid, then the KSS bound is violated in the bulk fluid. In other words the satisfaction of the KSS bound in the boundary fluid is a necessary condition for the satisfaction of the KSS bound in the bulk fluid.