A Thermodynamic Framework for Turing-Type Instabilities in Porous Media: Part I Theory

Abstract

Pattern formation in geological materials is commonly described using analogies to Turing-type reaction–diffusion systems, yet a unifying thermodynamic explanation remains elusive. Here we develop a multiscale, thermodynamically consistent framework for pattern-forming instabilities in porous media undergoing coupled thermo–hydro–mechanical–chemical–electrical processes. By extending irreversible thermodynamics to include configurational degrees of freedom and Onsager–Casimir reciprocal couplings, we show that morphing patterns emerge as universal non-equilibrium instabilities rather than system-specific bifurcations. Part I establishes the theoretical foundations and stability criteria; applications are presented in Part II.