Socio-Hydrodynamics: A Thermodynamic and Fluid-Mechanic Framework of Morality, Criminality, and Systemic Rupture

This paper introduces a novel, interdisciplinary framework that models the dynamics of human morality versus criminality through open-system thermodynamics and impact hydrodynamics. By mapping Maslow’s hierarchy of needs to concepts of exergy, entropy generation, and localized capillary potentials, we formalize how systemic neglect alters the socioeconomic landscape. We model the shift from moral adherence to survival-driven criminality as a discontinuous, first-order phase transition driven by a smoothly varying, continuous conjugate field via a saddle-node bifurcation of a bounded free energy landscape. The boundary condition for this behavioral rupture is defined using a sociological adaptation of the fluidic Weber number (We), offering a quantifiable, continuous threshold for when environmental catalysts trigger structural social disorganization. We explicitly incorporate modern urban sociology insights, demonstrating that physical population density operates as an inertial destabilizer under institutional neglect but undergoes a functional phase alignment to serve as a structural asset under robust social investment. Computational stability is established via logarithmic interior-point barrier potentials evaluated within stiff numerical frameworks, explicitly resolving prior computational artifacts, optimizing boundary constraints via a continuous hyperbolic tangent penalty function that preserves Jacobian continuity, and ensuring strict alignment with the Fluctuation-Dissipation Theorem.