The non-reciprocal entropy–production bound: proven cases, the Q = I premise, an exact reduction, and an open residual

Abstract:  Equilibrium intuition holds that added dissipation can only stabilise an attractor against noise-driven escape; we show this is a consequence of detailed balance, and that once detailed balance is broken a suitably directed dissipation increment can instead accelerate rare escape — but no faster than a sharp thermodynamic ceiling, , exact for linear (Ornstein–Uhlenbeck) dynamics with isotropic noise, dual to the thermodynamic uncertainty relation and saturated by a clean  geometry. We prove the bound, sharp constant included, in the small-coupling limit in every dimension, fully for two modes, and fully for  at all couplings by an exact, machine-verifiable rational certificate with no floating-point step;  is conjectured, supported by an exact reduction and -configuration numerics. Isotropic noise is load-bearing — for general noise the ratio is unbounded — so  is a genuine non-equilibrium condition rather than a normalisation. We validate the law in high-fidelity trajectory simulations of a non-reciprocal RLC circuit and an active-acoustic dimer, recovering the  rule and the entropy ceiling from trajectory data, and give pre-registered protocols for its laboratory measurement.