Abstract

Linking thermodynamic variables like temperature and the measure of chaos, the Lyapunov exponents, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we show that in thermalized flows that the Lyapunov exponent scales as the square-root of the temperature, in agreement with results from frustrated spin systems. This suggests an underlying universality and provides evidence for recent conjectures on the thermal scaling of the Lyapunov exponent. 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 the two through the dynamical structures of the flow. In the second half of the talk, I will discuss recent results on how thermalisation can be suppressed to obtain (numerical) estimates for and against blow-ups.  This work is done with Sugan Murugan, Dheeraj Kumar and Subhro Bhattacharjee.