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In phenomenological thermodynamics, the canonical coordinates of a physicalsystem split in pairs with each pair consisting of an extensive quantity and anintensive one. In the present paper, the quasi-thermodynamic fluctuation theoryof a model system of a large number of oscillators is extended to statisticalthermodynamics based on the idea to perceive the fluctuations of intensivevariables as the fluctuations of specific extensive ones in a"thermodynamically dual" system. The extension is motivated by the symmetry ofthe problem in the context of an analogy with quantum mechanics which is statedin terms of a generalized Pauli problem for the thermodynamic fluctuations. Thedoubled Boltzmann constant divided by the number of particles plays a similarrole to the Planck constant.

Fluctuations of intensive quantities in statistical thermodynamics