Kinetic equation for the one-particle distribution function of a classical gas: Derivation and comparison with the Boltzmann equation

Physica ◽  
1972 ◽  
Vol 58 (3) ◽  
pp. 445-469 ◽  
Author(s):  
B. Leaf
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Particle Distribution ◽  
Particle Distribution Function ◽  
The Boltzmann Equation ◽  
Classical Gas ◽  
The One

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 A construction of the general relativistic Boltzmann equation

1984 ◽  
Vol 7 (3) ◽  
pp. 591-597 ◽  
Author(s):  
P. Dolan ◽  
A. C. Zenios
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Simple Model ◽  
State Space ◽  
Differential Forms ◽  
Relativistic Boltzmann Equation ◽  
Dimensional State Space ◽  
General Relativistic ◽  
Invariant Differential

Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.

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