Derivation of Fokker-Planck equation from Schrodinger dynamics

2025/05/28 by Irfan Lone, Lone, Irfan
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Dynamics #FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2505.22693

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Fokker_Planck equation can be derived in a consistent manner through a microscopic approach based on a unified scheme of classical and quantum mechanics. Here we shall derive it through a purely quantum mechanical approach based on the reversible Schrodinger dynamics. We also give a brief discussion of the path integral representation of the Fokker_Planck equation in light of our derivation. We conclude that, because of the use of the representation of eigenstates of the time-independent Hamiltonian in our derivation, the thermodynamical entropy in this case must correspond to a coarse-graining of the quantum entropy.

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