Correlation Entropy and Power-Law Kinetics

Power-law kinetics are observed across a wide range of physical, chemical, biological, and engineering systems, yet the thermodynamic origin of the power-law exponent remains incompletely understood. This work proposes a thermodynamic hypothesis in which power-law behavior emerges naturally from correlation-dependent contributions to the Gibbs free energy. Rather than modifying the classical Boltzmann definition of entropy, a phenomenological Correlation Constant, χ, is introduced to quantify how accumulated microstate evolution influences the accessibility of future states. The resulting correlation entropy contribution produces a free-energy term that modifies the probability of subsequent transitions and leads naturally to power-law kinetic behavior. Positive values of χ correspond to cooperative evolution in which prior evolution promotes future evolution, while negative values correspond to self-limiting behavior in which prior evolution suppresses subsequent evolution. The conventional Arrhenius-Eyring description is recovered as the special case χ = 0. The resulting framework provides a thermodynamic interpretation of the power-law exponent, establishes a connection between entropy, free energy, and kinetic evolution, and offers a unified description applicable to degradation, relaxation, diffusion, fatigue, trapping, and other evolving processes. The present work is intended as a thermodynamic hypothesis motivating further experimental and theoretical investigation of correlation-dependent kinetics.