Entropy–Stress Phenomenological Model

We propose a phenomenological model that reconciles the entropy increase principle with the ordered nature of biological and social systems. Introducing entropy S as a generalized state variable, we decompose internal energy into a physical potential F(S) that decreases with entropy and a social potential G(S) that increases with entropy. The total energy is defined as E = F + G, and for open systems an external environmental energy W is included, E = F + G + W. We show that the total energy generally possesses a minimum in entropy space, corresponding to a least-stress state. Defining the internal stress as the entropy gradient of the internal potentials, U = d(F + G)/dS, we derive the dynamical relation U, dS/dt = d(E − W)/dt. This relation is formally equivalent to the force–flux structure of nonequilibrium thermodynamics, providing a unified description of stress, adaptation, and evolution in physical, biological, and social systems.