Stochastic Rupture via State-Dependent Rate Instability in the Reaction-Diffusion Field Theory

We propose a stochastic rupture mechanism for reaction-diffusion systems based on a state-dependent relaxation rate Γeff(χ) = Γ0 −λχ, which vanishes at the critical amplitude χc = Γ0/λ. This modification is exactly equivalent to a renormalization of the nonlinear coupling in the Langevin equation, preserving locality and the full Martin–Siggia–Rose–Janssen–De Dominicis (MSRJD) formalism. We identify the scalar field χ with the local informational saturation ratio χ = SvN/(η IBek) of the Stochastic Rupture (SR) framework [1], where SvN is the local von Neumann entropy and IBek is the Bekenstein bound of the enclosing causal-diamond region. Under the physically motivated condition α = λ/2, we derive—rather than postulate—the satu- ration feedback function F(χ) = (1 − χ) −1 as a direct consequence of the divergence of the zero-momentum field-fluctuation variance at the critical point. We further derive the homogeneous mean-field dynamics χ(t) and recover the rupture-time estimate τSR ∼ η/γ0 for nanoparticle superpositions. An analogy with overclocking and thermal throttling in computational processors provides physical intuition, in- cluding a speculative interpretation of quantum tunneling as time dilation between dynamically distinct regimes. A conceptual experiment using optically levitated nanoparticles to discriminate this framework from standard decoherence is proposed. The renormalization group analysis of this theory and the determination of its universality class are reserved for a companion work.