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nlin.CD2026
Emergence of Gamma-Type Upward-Phase Statistics in the Collatz Map: An Effective Poisson Process Mechanism
Weicheng Fu, Xiaobin Liu, Yisen Wang
The Collatz map is a simple deterministic transformation whose orbit structure remains highly nontrivial. A recent direction-phase decomposition partitions each orbit into upward a…
cond-mat.stat-mech2026
Boltzmann Distribution from Invariance of Coarse-Graining-Scale and Energy-Shift
Weicheng Fu, Yisen Wang, Yong Zhang +1
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical fac…