Fluctuations of intensive quantities in statistical thermodynamics

Abstract: In phenomenological thermodynamics, the canonical coordinates of a physical system split in pairs with each pair consisting of an extensive quantity and an intensive one. In the present paper, the quasi-thermodynamic fluctuation theory of a model system of a large number of oscillators is extended to statistical thermodynamics based on the idea to perceive the fluctuations of intensive variables as the fluctuations of specific extensive ones in a "thermodynamically dual" system. The extension is motivated by the symmetry of the problem in the context of an analogy with quantum mechanics which is stated in terms of a generalized Pauli problem for the thermodynamic fluctuations. The doubled Boltzmann constant divided by the number of particles plays a similar role to the Planck constant.