Heat capacity as a marker for shape and jamming transitions in active systems

What the math gives to ML

The paper provides a nonequilibrium calorimetric mechanism: a small temperature perturbation followed by relaxation produces an excess heat response whose peak identifies persistence-driven shape transitions and interaction-driven jamming transitions. Its transferable asset is not the lattice model itself, but the use of a dynamic response integral as a transition detector in a nonequilibrium process. In neural-network training, the effective temperature can be the SGD noise scale, Langevin-noise variance, dropout rate, or sampler temperature, while excess heat can be defined from transient optimizer dissipation after a controlled perturbation. This yields a falsifiable scheduler and diagnostic: response peaks should coincide with optimizer instability, representation collapse, or other sharp changes in training dynamics.