Statistical mechanics of transport coefficients

1976 ◽  
Vol 16 (3) ◽  
pp. 289-297 ◽  
Author(s):  
G. Vasu
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Statistical Mechanics ◽  
Particle Distribution ◽  
Transport Coefficients ◽  
Particle Distribution Function ◽  
Hydrodynamic Modes ◽  
The One ◽  
General Method

The problem of transport coefficients in statistical mechanics is reconsidered. A general method is given by which the hydrodynamical equations can straightforwardly obtained starting from the kinetic equation for the one-particle distribution function. From the statistical counterparts of the hydrodynamical equations so derived, the statistical expressions for the transport coefficients are immediately identified.Linearized hydrodynamic modes have recently been the object of very thorough reserach from the viewpoint of irreversible statistical mechanics; in particular, the Brussels school formalism has been used by Résibois to derive the eigenfrequencies of the hydrodynamical modes, whereby operatorial equations for transport coefficients have been obtained (Résibois 1970; see also the instructive book by Balescu (1975) on this subject).

scholarly journals Correlation magnetodynamics equations taking into account the uniaxial quadratic correction in the approximation of the one-particle distribution function

2021 ◽  
pp. 1-16
Author(s):  
Anton Valerievich Ivanov
Keyword(s):  
Distribution Function ◽  
Particle Distribution ◽  
Nearest Neighbors ◽  
Particle Distribution Function ◽  
Phase Transition Region ◽  
Simulation Results ◽  
The One ◽  
Bogolyubov Chain ◽  
New System ◽  
Good Agreement

The system of equations for correlation magnetodynamics (CMD) is based on the Bogolyubov chain and approximation of the two-particle distribution function taking into account the correlations between the nearest neighbors. CMD provides good agreement with atom-for-atom simulation results (which are considered ab initio), but there is some discrepancy in the phase transition region. To solve this problem, a new system of CMD equations is constructed, which takes into account the quadratic correction in the approximation of the one-particle distribution function. The system can be simplified in a uniaxial case.

scholarly journals Exact Statistical Mechanics of a One-Dimensional Self-Gravitating System

1971 ◽  
Vol 10 ◽  
pp. 56-72
Author(s):  
George B. Rybicki
Keyword(s):  
Distribution Function ◽  
Statistical Mechanics ◽  
Vlasov Equation ◽  
Total Mass ◽  
Particle Distribution ◽  
Spatial Density ◽  
One Dimensional ◽  
Large Numbers ◽  
Order Of Magnitude ◽  
The One

AbstractThe statistical mechanics of an isolated self-gravitating system consisting of N uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.

IRREVERSIBILITY IN RELATIVISTIC STATISTICAL MECHANICS

1994 ◽  
Vol 08 (29) ◽  
pp. 1847-1860 ◽  
Author(s):  
URI BEN-YA’ACOV
Keyword(s):  
Distribution Function ◽  
Statistical Mechanics ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Distribution Functions ◽  
Relativistic Dynamics ◽  
Direct Computation ◽  
Lagrangian Equations ◽  
The One

Relativistic statistical mechanics should be manifestly Lorentz covariant. In the absence of a Hamiltonian formalism in relativistic dynamics, a different approach which is based on the (Lagrangian) equations of motion is presented. Without any Liouville equation, this approach provides the direct computation of all the reduced n-particle distribution functions. The trajectories in the fully interacting system and ensemble averages are defined with respect to the parameters that fix the trajectories in the interaction-free limit. Irreversibility may emerge from microscopic dynamics due to the choice as to which part of the particles’ history — past or future — contributes to the interaction. Irreversibility is explicitly demonstrated in the evolution of the one-particle distribution function.

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