Scientific article / Periodica Polytechnica Chemical Engineering, 1961, Vol. 5, No 3, p. 219-243; No 4, p. 321-339.
Irreversible thermodynamics developed by Onsager is based on a double basis. It is for the most part of phenomenological character, but iu essential features it is also founded on statistical laws. The statistical considerations rest on the macroscopic fluctuation theory of thermodynamics. In this theory a systematical statement is valid, which can be formulated in a particular way — with the aid of the correlation functions in time, characterizing the fluctuations of macroscopic parameters — by the hypothesis of microscopic reversibility. However, this hypothesis holds strictly only for the equation of motion of individual particles, and the essential of it can be formulated in the following way: the equations of motion — either in classical or in quantum physics — are invariant against the transformation of sign of time t — –t. Assuming also that in an 'aged' system the average decay of fluctuations follows the ordinary macroscopic laws — which is a new hypothesis, and as has been shown by Becker not even realized in every case then the validity of Onsager's resp. Casimir's reciprocal relations is ensured by the form of microscopic reversibility expressed by the adequate correlation functions. Thus, at present, the Onsager's theory of irreversible thermodynamics, because of the above-mentioned hypothesis, should be considered as a particular and not quite natural complexity of phenomenological and statistical elements. Hence, the requirement to develop this theory on the basis of purely phenomenological and rigorously statistical principles is justified. Since already many attempts, which seem to be successful, have been made in the latter direction, therefore, we consider the phenomenological building up of the theory as our task. Our investigations were carried out by using such a general mathematical apparatus, which affords a possibility for the extension of Onsager's linear theory to a non-linear one.
