Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium

TL;DR

This paper investigates how time-reversal symmetry influences covariant Lyapunov vectors and local exponents in simple particle models, revealing discontinuities and symmetry effects in tangent space dynamics.

Contribution

It applies a new algorithm to compute covariant Lyapunov vectors in simple models, demonstrating the impact of time-reversal invariance on these quantities.

Findings

Time-reversal symmetry affects tangent space vectors.

Local covariant exponents show discontinuities.

Symmetry influences perturbation dynamics.

Abstract

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models, including an harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents. We also find that the local covariant exponents vary discontinuously along directions transverse to the phase flow.