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Investigated idea was actuated by the old opinion that a measurement of a quantum observable should be regarded a as a single deterministic sampling. But, according to the last decades studies, such observables are veritable random variables and their measurements must imply significant sets of statistical samplings. So one finds the indubitable caducity of the approached idea. Contiguously the respective finding allows to put into a new light the controversial questions like the Schrodinger's cat thought experiment or description of quantum measurements.

A presentation is given of the thermodynamic inequalities which, in the phenomenological theory, result from the condition that the correlation matrix of the equilibrium fluctuations is positive definite. These inequalities complete the set of thermodynamic inequalities deduced from the stability condition of thermodynamic equilibrium and from the Le Chatelier principle. Finally, the inequalities which are satisfied by the products of the dispersions and by the correlations between couples of thermodynamic variables are discussed. These inequalities are, in the author's opinion, similar to the uncertainty relations from quantum mechanics.

The fluctuations of thermodynamic systems in the presence of the fields are considered. The approach is of phenomenological nature and developed in a Gaussian approximation. The cases of a magnetizable continuum in a magnetoquasistatic field, as well as the so called discrete systems are used to exemplify the study. In the latter case one finds that the fluctuation estimators depend both on the intrinsic properties of the system and on the characteristics of the environment. Following earlier ideas of one of the authors we present a class of thermodynamic inequalities for the systems investigated in this paper. In the case of two variables these inequalities are nonquantum analogs of the well known quantum Heisenberg "uncertainty" relations. In this context, the fluctuation estimators support the idea that Boltzmann's constant k has the signification of a generic indicator of stochasticity for thermodynamic systems.

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