Effective field theory approach to odd elasticity

We have developed an effective field theory (EFT) framework applicable to active, non-equilibrium systems. Our approach to applying the EFT paradigm in the context of active matter departs from traditional methods that start with equations of motion. Instead, we postulate the form of the non-equilibrium steady state, which captures equal-time correlations. This approach offers an alternative pathway for constructing phenomenological models for driven and active matter. In this work, we apply our EFT formalism to problems in active solids—solids with active, non-conservative microscopic interactions that enable the material to perform work on its environment through quasi-static cycles of deformations. In the realm of odd elasticity, these active components contribute to the odd component of the static elastic modulus tensor. Specifically, we apply our formalism to a paper by Scheibner et al. [1], which established the equations of motion for odd elastic solids by postulating the most general stress tensor consistent with symmetry principles. By assuming there must be some notion of stationarity in this system, we discover additional constraints on certain active moduli. Our approach brings to light subtleties related to the nature of noise and time reversal symmetry breaking, leading to nontrivial results that have previously been overlooked.

[1] Scheibner, C., Souslov, A., Banerjee, D., Surówka, P., Irvine, W. T., & Vitelli, V. (2020). Odd elasticity. Nature Physics, 16(4), 475–480.