Title: Laplace-transform technique for deriving thermodynamic equations from the classical microcanonical ensemble
Abstract:A new method of deriving expressions for any thermodynamic-state function as an average of the appropriate microscopic dynamical functions over the microcanonical distribution is presented. The result...A new method of deriving expressions for any thermodynamic-state function as an average of the appropriate microscopic dynamical functions over the microcanonical distribution is presented. The results are valid for any system of classical particles interacting through a potential depending only on their relative positions and have a primary application to calculating thermodynamic quantities in molecular-dynamics computer-simulation studies. A Laplace-transform method is used to express any combination of energy and volume (or strain) derivatives of the microcanonical phase volume as averages of specific dynamical functions and their fluctuations. A unique result is the occurrence of the average reciprocal kinetic energy in these equations. These derivatives are then related to thermodynamic-state functions using the Legendre relations and the basic definition connecting the entropy to the phase-space volume. In particular, the complete microcanonical expressions for the adiabatic elastic constants are derived for the first time. The equations derived by this method are consistent with results from the literature pertaining to the classical microcanonical ensemble. The equivalence is obtained in the limit that the number of particles in the system approaches infinity, but the results diverge for systems with few particles. Numerical results from molecular-dynamics simulations of a simple model system are used to substantiate these points.Read More
Publication Year: 1985
Publication Date: 1985-11-01
Language: en
Type: article
Indexed In: ['crossref', 'pubmed']
Access and Citation
Cited By Count: 194
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