Coarse-Grained Dynamics of a Local Temporal Coherence Field

This article develops a minimal and internally consistent coarse-grained framework for describing the organization of temporal coherence in space and time. Temporal coherence is treated as a local, derived, and dimensionless diagnostic quantity that captures the finite-time persistence of correlations, without introducing new microscopic degrees of freedom or modifying existing physical theories. Starting from general physical constraints—locality, causality, boundedness, finite-time dissipation, and coherence maintenance—the work shows that the effective dynamics of a local temporal coherence field naturally falls into the reaction–diffusion universality class. A minimal evolution equation is proposed to describe how coherence propagates, decays, saturates, and is locally sustained at mesoscopic scales. The framework is complemented by a quasi-variational formulation that serves as an organizational tool for understanding stationary regimes and stability. Stationary solutions of the coherence dynamics give rise to spatially structured coherence profiles, which admit an effective geometric interpretation in the sense that coherence gradients act as organizing structures influencing physical processes. Importantly, the coherence field is not interpreted as a fundamental physical entity. The approach does not propose a new theory of gravity, does not modify quantum mechanics or general relativity, and does not introduce new dynamical laws. Instead, it provides a unifying organizational language for finite-time coherence phenomena that remains fully compatible with established microscopic descriptions. Within the broader finite-time invariant / Ranesis framework, this work bridges purely diagnostic notions of coherence with effective spatial organization, preparing the ground for later studies on coherence gradients, emergent geometry, and finite-time conservation structures.