Protocol-Dependent Jamming Entropy Theory (PDJET): Maximizing Effective Packing Density via Random Fluctuations in Hard-Particle Systems

This paper proposes the ’Protocol-Dependent Jamming Entropy Theory (PDJET)’, which elucidates the physical mechanism by which random fluctuation protocols maximize local packing density more efficiently than deterministic ordering in many-body hard-particle systems. By extending the Edwards ensemble for granular matter and incorporating the Universal Rough Operator Algebra (UROA), we construct an effective free energy functional that formulates the thermodynamic trade-off between the order-constraining Lagrange multiplier(λ) and compactivity (X). Furthermore, Monte Carlo packing results of non-spherical particles (ellipsoids) and logarithmic compaction experimental data driven by tapping are quantitatively interpreted through the generalized isostatic condition and Fokker-Planck Langevin dynamics. Ultimately, we demonstrate that disorder-driven local optima in a finite container reach higher densities within realistic time scales than the global optimum directed towardperfect crystal structures.