Abstract Non-equilibrium systems with spatial heterogeneities, such as temperature gradients in thermal transients, could be analyzed through the Local Thermodynamic Equilibrium (LTE) approximation, where entropy is computed as an integral of local contributions. However, this perspective often overlooks global correlations induced by the gradient. This work introduces a framework that models variations of an intensive parameter β ( r ) over a structured domain Ω, treating the system as a determ