Differentiable Bureaucracy: A Non-Newtonian Information-Fluid Approach to Institutional Stagnation

We present a complete, coordinate-invariant continuum mechanics framework modelingcorporate and governmental bureaucracies as non-Newtonian, shear-thickening, entropy-compressible informational fluids. By extending the classical Herschel-Bulkley viscoplasticmodel via a Papanastasiou exponential regularization parameter, we rigorously characterizethe unyielded plug-flow regions typical of middle management. We introduce the KafkaNumber (Ka), a dimensionless ratio quantifying the dominance of administrative yieldstress over structural operational momentum. We show that at Ka≥1, a discrete jammingtransition occurs, freezing the institutional velocity field. The phenomenon of “managerial rod-climbing” is mathematically derived by upgrading the framework to a viscoelastic Oldroyd-Bconstitutive model, mapping the first and second normal stress differences to the Weissenbergeffect. Finally, we resolve boundary layer singularities at the compliance perimeter using aRobin flux boundary condition and validate our framework through an instrumental variableapproach utilizing the exogenous shock of a corporate-wide font migration.