Backward and covariant Lyapunov vectors and exponents for hard disk systems with a steady heat current

TL;DR

This paper extends covariant Lyapunov analysis to systems with heat currents, analyzing how Lyapunov exponents and modes behave under nonequilibrium conditions, revealing asymmetries and oscillations in mode frequencies and angles.

Contribution

It generalizes covariant Lyapunov vectors and exponents to nonequilibrium systems with heat currents, providing new insights into mode behavior and angular distributions.

Findings

Lyapunov exponents change with heat current.

Hydrodynamic Lyapunov modes are analyzed and compared.

Mode frequencies and angles exhibit asymmetry and oscillations.

Abstract

The covariant Lyapunov analysis is generalised to systems attached to deterministic thermal reservoirs that create a heat current across the system and perturb it away from equilibrium. The change in the Lyapunov exponents as a function of heat current is described and explained. Both the nonequilibrium backward and covariant hydrodynamic Lyapunov modes are analysed and compared. The movement of the converged angle between the hydrodynamic stable and unstable conjugate manifolds with the free flight time of the dynamics is accurately predicted for any nonequilibrium system simply as a function of their exponent. The nonequilibrium positive and negative $\LP$ mode frequencies are found to be asymmetrical, causing the negative mode to oscillate between the two functional forms of each mode in the positive conjugate mode pair. This in turn leads to the angular distributions between the conjugate modes to oscillate symmetrically about $\pi/2$ at a rate given by the difference between the positive and negative mode frequencies.