A Memory-Integrated Entropy-Decay Framework for Irreversible Field Evolution

This paper proposes an entropy-based framework for describing irreversible physical processes by replacing conventional time and space variables (t,x)(t, x)(t,x) with entropic coordinates (τ,Ψ), representing decay progression and entropy propagation. The formulation begins with a reversible wave-like relation and extends to irreversibility through stochastic coupling and a memory kernel K(τ−τ′), yielding a nonlinear, non-Markovian field equation. Four parameters—α, β, γ, and δ—govern curvature-driven propagation, oscillatory behavior, stochastic interactions, and damping, respectively. The model unifies reversible and irreversible dynamics within a single formalism and recovers classical behavior in the limit of negligible memory. This theoretical framework provides a structural approach to entropy-driven evolution across complex systems, with potential applications in heat transfer, phase transitions, and non-equilibrium dynamics.