Journal Article10.1063/1.1740082
Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids
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TL;DR: In this article, the authors apply the procedure developed in a previous paper of the same main title to the specific case of irreversible processes in fluids, where the gross variables are chosen to be a finite number of the plane-wave expansion coefficients of the local particle, momentum and energy densities.
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Abstract: The procedures developed in a previous paper of the same main title are applied to the specific case of irreversible processes in fluids. The gross variables are chosen to be a finite number of the plane‐wave expansion coefficients of the local particle, momentum and energy densities. As an example, the gross variables describing the local particle density are ∑ i=1Nexpik·xi, where pi and xi are the momentum and position of the ith molecule and N the total number. k runs over a finite number of values which are all small compared to the reciprocal mean distance between molecules. The phenomenonological equations are derived and expressions are given for the viscosity, diffusion, and heat conductivity in terms the autocorrelation coefficients of certain phase functions. These expressions are supposed to be valid for both liquids and gases. They are shown to coincide with the Chapman‐Enskog expressions for dilute gases.
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References
The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics
J. H. Irving,John G. Kirkwood +1 more
TL;DR: In this article, the contributions of intermolecular force to the stress tensor and heat current density are expressed as quadratures of the density and current density in the configuration space of a pair of molecules.
2.5K
The Statistical Mechanical Theory of Transport Processes I. General Theory
TL;DR: In this paper, the authors sketched a general statistical mechanical theory of transport processes; e.g., diffusion, heat transfer, fluid flow, and response to time-dependent external force fields.
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Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena
TL;DR: In this paper, two principles of a statistical mechanics of time-dependent phenomena are proposed and argued for, namely, the proper mathematical object to describe the physical situation is the stationary random process specified by the ensemble of time series ai(Xt)i=1−s and the distribution ρ(X).
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