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In this work a geometrical representation of equilibrium and near equilibrium statistical mechanics is proposed. Using a formalism consistent with the Bra-Ket notation and the definition of inner product as a Lebasque integral, we describe the macroscopic equilibrium states in classical statistical mechanics by "properly transformed probability Euclidian vectors" that point on a manifold of spherical symmetry. Furthermore, any macroscopic thermodynamic state "close" to equilibrium is describeddoi:10.26434/chemrxiv.7217819 fatcat:wjkqyoz2abe7fdlcgtb47eayee