Odd elastohydrodynamics: non-reciprocal living material in a viscous fluid*

Microswimmers are a central target in understanding the biological system from a physical point of view. Microswimmers consume energy to generate shape change to propel themselves at low Reynolds numbers. In this talk, we introduce the concept of odd elasticity, a relatively new framework for describing the non-equilibrium state of matter and an extension of linear elasticity, to the field of microswimmer elastohydrodynamics. We start by presenting the simplest theoretical models, three-sphere swimmer and Purcell's three-link swimmer, and inflict not only ordinal elasticity but also odd elasticity. We demonstrate that the odd-elastic properties enable the swimmer to exhibit average locomotion without any prescribed actuation and discuss the role of the thermal fluctuations [1,2]. Furthermore, we generalize our concrete odd elastic microswimmer to odd elastohydrodynamics, describing a general swimmer subjected to periodic deformations by extending into a non-linear regime [3]. Through the analysis of Chlamydomonas flagella waveforms and experimental data for human sperm, we demonstrate the wide applicability of a nonlocal and non-reciprocal description of internal interactions within living materials in viscous fluids, offering a unified framework for active and living matter physics.