Emergent behaviors of relativistic thermodynamic flocks with Synge energy

Abstract

Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale models, we introduce a polyatomic classical model and its relativistic counterpart based on the Synge energy, and analyze their large-time behavior. The relativistic formulation provides a physically consistent setting for multi-species systems where inertia and internal energy depend on temperature, as occurs in astrophysical plasmas or relativistic fluids. Using the entropy principle, we derive uniform lower bounds for temperature and establish asymptotic flocking under various communication kernels. For nearly constant interactions, flocking emerges from arbitrary initial data. The results clarify how thermodynamic effects and relativistic corrections modify the emergence of coherent motion in particle systems, bridging kinetic theory, relativistic fluid mixtures, and collective dynamics.