Non-Equilibrium Thermodynamics of Active Matter Systems

Abstract

Active matter systems, composed of self-propelled units that continuously consume energy to move, sit
fundamentally outside equilibrium statistical mechanics, yet a quantitative link between collective behaviors such as
clustering and the entropy production rate driving them has remained only partially established. We performed
Brownian dynamics simulations of self-propelled disks interacting via a short-range repulsive potential, computing
the stochastic entropy production rate from individual particle trajectories across 40 combinations of Péclet number
(2 to 150) and area fraction (0.20 to 0.70), with 2,000 particles per simulation and 60 independent replicates per
parameter combination. Entropy production rate per particle increased monotonically with Péclet number at fixed
density, from 0.34 k_B/tau at Pe = 2 to 18.7 k_B/tau at Pe = 150, but showed a pronounced non-monotonic
dependence on area fraction at fixed high Péclet number, peaking at an intermediate area fraction of 0.45 (11.2
k_B/tau at Pe = 100) before declining by 34% at area fraction 0.70 (7.4 k_B/tau), coinciding with the onset of
motility-induced phase separation identified independently from the local density distribution. The entropy
production rate peak at intermediate density correlated closely with the largest cluster size relative to system size,
which itself peaked at area fraction 0.45 (mean largest-cluster fraction 0.61 ± 0.04), suggesting cluster boundary
dynamics, rather than either the dilute gas phase or the dense jammed phase, are the dominant dissipative process
in this regime. A scaling analysis across the full Péclet-density parameter space found entropy production rate
scaled as Pe^1.82 ± 0.06 in the dilute regime (area fraction < 0.30) but as Pe^1.31 ± 0.09 in the phase-separated
regime (area fraction >= 0.55), a statistically significant difference (bootstrap 95% CI for exponent difference: 0.31
to 0.71) indicating that caging and cluster formation suppress the rate at which activity converts into dissipation.
These results establish a quantitative, trajectory-level link between a purely mechanical order parameter, cluster
size, and a purely thermodynamic quantity, entropy production rate, in a canonical active matter model, with
implications for estimating the energetic cost of self-organization in both synthetic active colloids and, more
speculatively, biological collective systems operating in comparable density and activity regimes.