# Many-body Chaos in Thermalised Fluids

## TL;DR

This paper demonstrates that in thermalised fluids, the Lyapunov exponent scales with the square root of temperature, revealing a universal relationship and connecting chaos measures with thermodynamic variables.

## Contribution

It proves the universal scaling law $ ext{Lyapunov exponent} \, \propto \sqrt{T}$ in thermalised fluid flows using nonlinear fluid equations in one and three dimensions.

## Key findings

- Lyapunov exponent scales as √T in thermalised flows
- Universal relation between chaos and temperature in fluids
- Reconciliation of equilibration and out-of-equilibrium chaos effects

## Abstract

Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we prove that in thermalised flows $\lambda \propto \sqrt{T}$, in agreement with results from frustrated spin systems. This reveals an underlying universality and provides evidence for recent conjectures on the thermal scaling of $\lambda$. We also reconcile seemingly disparate effects -- equilibration on one hand and pushing systems out-of-equilibrium on the other -- of many-body chaos by relating $\lambda$ to $T$ through the dynamical structures of the flow.