Entropy of state transitions in macroscopic active matter

The extension of thermodynamic principles to active matter remains a challenge due to the non-equilibrium nature inherent to active systems. In this study, we introduce a framework to assess entropy in our minimal macroscopic experiment based on the utilized degrees of freedom. Using motorized spheres as active particles, we demonstrate that the system transitions between distinct active states. Analogous to the phase transition in classic solids, liquids, and gases, each phase is characterized by a quantifiable change in entropy. We show that the corresponding phase transitions are accompanied by discrete jumps in entropy, resulting from newly utilized degrees of freedom. Our findings reveal that active matter can exhibit phase transitions analogous to classical thermodynamic systems, quantifiable in terms of their entropy and temperature. By bridging equilibrium thermodynamics and active matter, this work shows how underlying principles extend to complex, living systems.