Equilibrium Energy Partition and Planck–Like Universality in Galactic Rotation Curves

This work investigates the observed universality of galactic rotation curves from the perspective of equilibrium energy partition in dynamically relaxed, self-gravitating systems.We introduce a phenomenological framework in which radial distributions of effective mass and orbital energy are organized on a coarse-grained virial manifold, leading naturally to flat rotation behavior without invoking specific dark-matter microphysics. Motivated by equilibrium statistical-mechanics analogies and Planck-like universality concepts, the study formulates a minimal variational principle incorporating global stability constraints and configurational energy balance.The resulting equilibrium-shaped radial families reproduce the scaling required for approximately constant orbital velocities across extended galactic radii. This framework is not proposed as a replacement for dark matter or modified gravity, but rather as a unifying thermodynamic-style interpretation explaining why simple near-universal functional forms emerge in galactic dynamics.