Symmetry, Thermodynamics and Topology in Active Matter

Abstract

This article summarizes some of the open questions in the field of active matter that have emerged during Active20, a nine-week program held at the Kavli Institute for Theoretical Physics (KITP) in Spring 2020. The article does not provide a review of the field, but rather a personal view of the authors, informed by contributions of all participants, on new directions in active matter research. The topics highlighted include: the ubiquitous occurrence of spontaneous flows and active turbulence and the theoretical and experimental challenges associated with controlling and harnessing such flows; the role of motile topological defects in ordered states of active matter and their possible biological relevance; the emergence of non-reciprocal effective interactions and the role of chirality in active systems and their intriguing connections to non-Hermitian quantum mechanics; the progress towards a formulation of the thermodynamics of active systems thanks to the feedback between theory and experiments; the impact of the active matter framework on our understanding of the emergent mechanics of biological tissue. These seemingly diverse phenomena all stem from the defining property of active matter -assemblies of self-driven entities that individually break timereversal symmetry and collectively organize in a rich variety of nonequilibrium states.

Flow transitions and length scales of a channel-confined active nematic

“…The governing equations are solved in a rectangular domain using a hybrid lattice Boltzmann algorithm 42,45 . This method involves sequential temporal updates using a lattice Boltzmann method for the Navier-Stokes equations ( 1) and ( 2) and a method of lines for the Q evolution equation (3). The grid and time resolutions are chosen as unity following the usual framework of lattice Boltzmann approaches 47 .…”

“…Active nematics are fluids that comprise anisotropic active entities that consume available energy and perform mechanical work. This energy throughput is often reflected as self propulsion of the active particles, they exert a stress field on the surrounding medium, thus maintaining the system in a non-equilibrium state [1][2][3][4] . Active nematics include a variety of biological systems such as bacterial suspensions [5][6][7][8][9] , collections of cells [10][11][12] , and microtubules and motor protein mixtures 13,14 , and synthetic systems such as vibrating granular rods 15,16 and phoretic active particles 17 .…”

Spatial confinement affects the heterogeneity and interactions between shoaling fish

“…Therefore, this search for the relationship between interactions and bulk behavior is also critical for defining collective systems as living materials in-and-of themselves. In particular, these living materials are fundamentally non-equilibrium due to the local consumption of energy by each entity, and definitions of the mechanical [23][24][25] or thermodynamic 26,27 properties of these systems will help determine the material possibilities of these types of systems.…”

Fluctuation-induced dynamics of nematic topological defects

“…Topological defects in nematics have recently been found to be at the core of many biological functions, e.g. cell extrusion in mammalian epithelia [10], neural mound formation [12], and limb origination in the simple animal Hydra [6] (see [1,13,14] for recent reviews on physical and biological significance of topological defects).…”