Thermodynamics of active matter with internal degrees of freedom

Abstract Complex functionalities in biological systems arise from rich internal state dynamics that allow them to adjust behavior in response to environmental cues. While active matter is widely used to model such systems, most existing frameworks ignore these internal mechanisms and rely on prescribed forces or rules, without capturing how energy is transduced. Here, we introduce a thermodynamically consistent framework for active matter whose units possess arbitrarily complex internal state spaces. Internal states are represented as Markov networks, with motility driven by designated power strokes, enabling directed motion and adaptive dynamics. Enforcing local detailed balance, our approach provides direct access to system thermodynamics, allowing explicit calculation of the dissipation associated with coupled microscopic and mesoscopic degrees of freedom. Leveraging network theory, we reduce the number of tracked variables by expressing the dissipation rate in terms of a minimal basis of fundamental cycles. We further extend the description to a hydrodynamic continuum theory and find closed expressions for the local and global dissipation rates. We illustrate the framework with a prototypical active particle with a multicyclic internal state space that is confined by a harmonic external potential.