Variational principle and phase space measure in non-canonical coordinates

Alessandro Sergi

Abstract


Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of coordinates. This shows that the geometry of non-canonical phase space is non trivial even if dynamics has no compressibility.

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DOI: http://dx.doi.org/10.1478/C1A0501003