# Mechanics of active surfaces

## TL;DR

This paper develops a comprehensive covariant framework for understanding the mechanics of active surfaces, incorporating forces, torques, symmetry breaking, and active contributions to surface properties and instabilities.

## Contribution

It introduces a fully covariant theory of active surface mechanics, including new active terms and symmetry considerations, extending passive surface models.

## Key findings

- Active terms modify surface tension, bending modulus, and spontaneous curvature.
- Surfaces with certain symmetries can exhibit broken up-down, chiral, or planar-chiral symmetry.
- The theory predicts shape instabilities driven by active processes.

## Abstract

We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or reconstituted active systems on surfaces. We introduce forces and torques acting on a surface, and derive the associated force balance conditions. We show that surfaces with in-plane rotational symmetry can have broken up-down, chiral or planar-chiral symmetry. We discuss the rate of entropy production in the surface and write linear constitutive relations that satisfy the Onsager relations. We show that the bending modulus, the spontaneous curvature and the surface tension of a passive surface are renormalised by active terms. Finally, we identify novel active terms which are not found in a passive theory and discuss examples of shape instabilities that are related to active processes in the surface.