Thermodynamic Work Functions and their Relation to Relative Entropy and Kullback-Leibler Divergence

<jats:p>Thermodynamic work functions formalize the energetic principles governing macroscale process trajectories and microscopic equilibria, symbolizing directional energy vectors defined along a one-dimensional process path unit vector. While macroscopic processes remain inherently irreversible, chemical transformations are governed by reversible microscopic energy modifications embedded within a macroscopic host system. The non-dimensionalized vector representation of the chemical work function maps directly to the Kullback-Leibler divergence layout, replacing the conventional Gibbs free energy formulation. This statistical mechanism operates independently of the second law, establishing the fourth law of thermodynamics as a distinct principle that initiates changes in the intensive states to drive macroscopic boundary gradients. The framework formalizes the physical co-existence of macroscopic irreversible dissipation, general microscopic reversibility, and localized spontaneous entropy reduction within structured configurations. The scaling invariant nature of this information-theoretic subtraction layout unifies the description of non-cohesive reference states, cohesive molecular phases, and long-range gravitational fields.</jats:p>