This paper presents Nobre Kinetics as a discrete, deterministic dynamical system of five equations. The formal results demonstrated are: (T1) convergence in at most (n−3)/2 steps via Lyapunov function; (T2) uniqueness of the trajectory for each n; (C1) exact length K(n) = (n−3)/2 for every odd prime n > 3; (C2) thermodynamic bound C(n) ≥ ((n−3)/2)·kʙ·T·ln 2 for any physical implementation of this kinetics at temperature T > 0. The bound C(n) is the thermodynamic cost of this specific dynamics, not a universal bound on the primality problem. The absence of a Hamiltonian generating this kinetics via gradient flow is established formally (P2). The central open question, which remains unanswered, is: does there exist a natural physical system whose redistribution dynamics of identical units under conservation is isomorphic to equations (1)–(5)?
Thiago Braga Nobre (Thu,) studied this question.