Simple holographic dual of the Maxwell-Cattaneo model and the fate of KMS symmetry for nonhydrodynamic modes

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>τ</a:mi> </a:math> , 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 assumptions, we find that effective field theories featuring nonhydrodynamic modes exhibit a generalized form of Kubo-Martin-Schwinger symmetry, which reduces to the canonical form only in the hydrodynamic limit.