Gauge anomaly and visible dissipation bounds in active matter.

Abstract

We formulate a nonequilibrium gauge theory for active many-body steady states and derive rigorous, data-accessible lower bounds on dissipation. The setting is an overdamped translational sector on an extended one-particle state space, where internal variables may encode orientations, species, or other hidden degrees of freedom. We show that broken detailed balance enters the response to spatial shift generators through a current-induced gauge anomaly, while the generator algebra itself remains unchanged. At the one-body level, this yields a localized hyperforce balance and an exact projection theorem that decomposes the translational entropy production into visible and hidden non-negative parts at arbitrary retained one-particle resolution. The resulting bounds depend only on equal-time one-body densities, currents, and force densities, and therefore avoid time reversal and full trajectory inference. For active Brownian particles, we show that the physically relevant retained variables are position and orientation, not position alone: position-only fields can be entirely blind to irreversibility even in mechanically static steady states. Brownian-dynamics simulations of ideal, homogeneous interacting, and slit-confined active Brownian particles confirm the theoretical predictions. Our results connect gauge response, coarse graining, and measurable irreversibility in active matter.