2025/10/31 by Partha Ghose, Ghose, Partha
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2510.27170
openalex publication_date 2025/10/31 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/28
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification ℏ = mσ. Ghose's interpolating equation introduces a continuous parameter λ that suppresses the quantum potential Q[ψ] and yields a smooth transition between quantum (λ=0) and classical (λ=1) regimes. In this short note, we show that the Koopman--von Neumann (KvN) Hilbert-space formulation of classical mechanics emerges naturally as the λ→ 1 limit of this stochastic σ--λ hierarchy. The KvN phase-space amplitude provides an operator representation of the classical Liouville equation, while the λ parameter acts as a projection flow from the complex projective Hilbert manifold ℂPn to its classical quotient ℂP^*/U(1), implementing phase superselection. This unified picture links quantum, stochastic, and classical dynamics within a single continuous framework.