A Universal Rotational Potential Law: From Molecular Thermodynamics to Galactic Dynamics

We propose a universal rotational potential law expressed as which governs the equilibrium structure of confined rotational systems across all physical scales—from molecular thermodynamics to atomic orbits and galactic dynamics. This relation, while reminiscent of Keplerian orbital motion, emerges from fundamental geometrical and energetic balance conditions that extend beyond gravitational mechanics. Through dimensional analysis, thermodynamic interpretation, and astrophysical application, we demonstrate that the same potential-angular velocity scaling describes diverse systems from heated gas in laboratory flasks to galaxy rotation curves, without invoking dark matter or modified gravity. An additional appendix introduces the principle of compensatory symmetry, suggesting that physical evolution is governed by intrinsic balancing mechanisms. This work proposes a unifying framework for interpreting rotational dynamics, energy distribution, and entropy-driven structure formation. Author:Tetsuo Konno(今野哲夫) https://orcid.org/0009-0002-1842-7865 [email protected]