Topological packing statistics as a framework for nonequilibrium thermodynamics

Living systems operate far from equilibrium, with individual components continuously consuming energy to perform various functions. Developing thermodynamics metrics is crucial for quantifying the energy costs of these processes and understanding system-wide phase transitions. Advances in stochastic thermodynamics have set lower bounds on entropy production rates, motivating the adaptation of thermodynamic tools for nonequilibrium characterization. Here, we explore topological packing statistics as a framework to quantify nonequilibrium dynamics and thermodynamics, using living chiral crystals of starfish embryos [1] as a model system. Building on a graph-theoretic method [2], we extract individual network statistics for each embryo in the living chiral crystal, representing a “topological microstate” at a given time. By computing the topological distance of each microstate from a hexagonally ordered “ground state”, we achieve a coarse grained representation of the system, enabling us to probe phase space dynamics and a possible effective temperature. Combining simulations with experimental data, we examine how topological network statistics capture nonequilibrium and steady state behavior. Our results offer insights into the role of topological structures in encoding complex dynamics, potentially advancing the thermodynamic characterization of living systems.

[1] Tan et al. Nature Vol. 607, 287-293 (2022).

[2] Skinner et al. Sci. Adv. Vol. 9, Issue 36, eadg1261 (2023).