2013/08/06 by Shoichi Ichinose, Ichinose, Shoichi
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Physics and Python Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1308.1238
openalex publication_date 2013/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the \it velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. \it Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is \it emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does \it not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.