The phase space description of a system of N point masses confined to a rectangular box is shown to be equivalent to knowledge of a minimal set of 6N complex Fourier coefficients associated with the discrete distributions of matter and momentum. The corresponding real-valued truncated Fourier series yield continuum densities of particle number and momentum at a specific length scale, min . Continuum descriptions at any scale >min correspond to further truncation of these series. Attention is drawn to the relevance of the results to recent investigations of reproducible macroscopic behaviour, at a given pair and - of length time scales, using projection operator methodology.
|Number of pages||13|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 10 Aug 2001|
- Fourier coefficients
- reproducible macroscopic behaviour
- projection operator methodology