Monte Carlo in the microcanonical ensemble

Integration of the kinetic degrees of freedom

Considering a system of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. N \right. } identical particles, with total energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. H \right. } given by:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H = \sum_{i=1}^{3N} \frac{p_i^2}{2m} + U \left( X^{3N} \right). }

where the first term on the right hand side is the kinetic energy, whereas the second one is the potential energy (function of the position coordinates)

From the partition function in the microcanonical ensemble we can integrate

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