Simple holographic dual of the Maxwell-Cattaneo model & the fate of KMS symmetry for non-hydrodynamic modes

TL;DR

This paper develops a simple holographic dual for the Maxwell-Cattaneo model, capturing finite relaxation effects in diffusion and revealing that non-hydrodynamic modes obey a generalized KMS symmetry, extending the understanding of intermediate time-scale dynamics.

Contribution

It constructs a holographic dual of the Maxwell-Cattaneo model and demonstrates the generalized KMS symmetry for non-hydrodynamic modes, advancing holographic modeling of finite relaxation phenomena.

Findings

Holographic dual of the Maxwell-Cattaneo model established

Non-hydrodynamic modes obey a generalized KMS symmetry

Finite relaxation effects captured in holographic framework

Abstract

Diffusion, as described by Fick's laws, governs the spreading of particles, information, data, and even financial fluctuations. However, due to its parabolic structure, the diffusion equation leads to an unphysical prediction: any localized disturbance instantaneously affects the entire system. The Maxwell-Cattaneo (MC) model, originally introduced to address relativistic heat conduction, refines the standard diffusion framework by incorporating a finite relaxation time $\tau$, associated with the onset of local equilibrium. This modification yields physically relevant consequences, including the emergence of propagating shear waves in liquids and second sound in solids. Holographic methods have historically provided powerful tools for describing the hydrodynamics of strongly correlated systems. However, they have so far failed to capture the dynamics governed by the MC model, limiting their ability to model intermediate time-scale phenomena. In this work, we construct a simple holographic dual of the Maxwell-Cattaneo model and rigorously establish its equivalence through a combination of analytical and numerical techniques. As an important byproduct of our analysis, and contrary to previous ad-hoc assumptions, we find that effective field theories featuring non-hydrodynamic modes exhibit a generalized form of Kubo-Martin-Schwinger (KMS) symmetry, which reduces to the canonical form only in the hydrodynamic limit.