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تسجيل مستخدم جديدVelocity-Field Theory, Boltzmanns Transport Equation, Geometry and Emergent Time
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تأليف
Shoichi Ichinose
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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 properties of the fluid matter (fluid particles) appear as the density and the viscosity. {it Statistical fluctuation} is examined, and is clearly discriminated from the quantum effect. The time variable is {it emergently} introduced through the computational process step. Besides the ordinary potential, the general velocity potential is introduced. The collision term, for the Higgs-type velocity potential, is explicitly obtained and the (statistical) fluctuation is closely explained. The system is generally {it non-equilibrium}. The present field theory model does {it not} conserve energy and is an open-system model. One dimensional Navier-Stokes equation, i.e., Burgers equation, appears. In the latter part of the text, we present a way to directly define the distribution function by use of the geometry, appearing in the energy expression, and Feynmans path-integral.
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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) fi
elds 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 Burgers 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 Feynmans path-integral.
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