Onsager's variational principle for nonreciprocal systems with odd elasticity

TL;DR

This paper develops a systematic method using Onsager's variational principle to derive nonreciprocal dynamical equations for active systems with odd elasticity, revealing the physical origin of odd elastic constants in nonequilibrium conditions.

Contribution

It introduces a new approach to derive nonreciprocal equations for active matter with broken time-reversal symmetry using Onsager's variational principle.

Findings

Derived nonreciprocal equations for active systems with odd elasticity.

Showed odd elastic constants are proportional to nonequilibrium forces and friction.

Provided a systematic framework for modeling active matter with broken time-reversal symmetry.

Abstract

Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the nonreciprocal set of equations for the material coordinates. The obtained nonreciprocal equations manifest the physical origin of the odd elastic constants that are proportional to the nonequilibrium force and the friction coefficients. Our approach offers a systematic and consistent way to derive nonreciprocal equations for active matter in which the time-reversal symmetry is broken.