Scaling of entropy production under coarse graining in active disordered media

Energy Cost for Flocking of Active Spins: The Cusped Dissipation Maximum at the Flocking Transition

“…The two-site (and three-site) AIM provides a useful approach for understanding spatially extended nonequilibrium systems without completely going to the mean-field limit, which is an equilibrium limit unable to capture many nonequilibrium properties such as energy dissipation. Given that the two-site AIM can be considered as a coarse-grained version of the full AIM, it will be interesting to investigate what is the appropriate coarsegraining procedure that preserves the dissipation characteristics in particular the cusped maximum behavior, and whether there is scaling law for the dissipation as suggested by recent studies of general reaction networks [28][29][30]. Finally, the energy-speed-sensitivity trade-off uncovered here may provide a useful perspective for understanding dynamics of natural flocks and designing optimal control of artificial flocks.…”

“…Namely, it does not give the (physical) heat dissipation rate, and an alternative term "information EPR" has been proposed to differentiate it from the microscopic EPR, which has unambiguous thermodynamic interpretation [25][26][27]. The reason behind this discrepancy is that coarse-graining drastically decreases the dissipation rate [28][29][30], which means that macroscopic theories tend to dramatically underestimate the energy dissipation. Therefore, it is fundamentally important to elu-cidate the energy cost of flocking using a microscopic model, which gives the "true" heat dissipation, despite existing work using hydrodynamic approaches [31,32].…”

The energy cost for flocking of active spins

“…In the latter case, irreversibility is measured by the information entropy production rate [23][24][25], but its connection to the heat dissipation rate is usually lost unless thermodynamic consistency is ensured, for instance, by relying on linear irreversible thermodynamics [26]. The energy dissipation also depends on coarsegraining [27][28][29], which makes it difficult to determine the true dissipation rate from coarse-grained field theories. Microscopic models, however, offer a more straightforward thermodynamic interpretation as energy dissipation (heat) can be determined directly from entropy production rate at the single-particle level.…”

“…It is quite remarkable that highly nontrivial characteristics of the dissipation profile such as the cusped maximum at the critical point can be captured and explained by the simple two-site AIM. Given that the two-site AIM can be considered as a coarse-grained version of the full AIM, it will be interesting to investigate what is the appropriate coarse-graining procedure that preserves the dissipation characteristics in particular the cusped maximum behavior, and whether there is scaling law for the dissipation as suggested by recent studies of general reaction networks [27][28][29]. Another possible direction to explore is to extend this study to flocking theories with continu-ous symmetry and off-lattice models [6][7][8].…”