Fluctuations and Thermodynamic Inequalities

Abstract

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.

Fluctuations in the presence of fields: Phenomenological Gaussian approximation and a class of thermodynamic inequalities

“…. From (28) it directly results that in the absence of field (δT ) 2 has the previously known expression [7][8][9].…”

“…where (α −1 ) ab are the elements of the inverse of the matrix α given by (9). Q m = Q m (X a )] the fluctuations are characterized by the correlations…”

“…As in the case of fluctuations in the absence of fields [9] the correlations (11) constitute a real, symmetric and non-negative definite matrix. Then from (11) one obtains the relation:…”

“…Our description is done in a phenomenological manner. We will appeal to usual procedures of phenomenological theory [2,4,7,8] as well as some ideas inspired by our earlier works on fluctuations [9,10].…”

“…Afterward we will investigate briefly the questions connected with the fluctuations in discrete systems in the presence of magnetic field. By using the results of the alluded investigations in a next section we will introduce a new class of thermodynamic inequalities, in a manner similar with the one developed in [9].…”