To the derivation of Onsager reciprocity relations in the context of non-additive statistics

In the framework of non-extensive Tsallis thermodynamics, Onsager symmetry relations for kinetic coefficients in linear regression equations for even and odd small fluctuations of macroscopic state parameters are derived. These relations reflect at the macroscopic level the invariance of microscopic equations of motion with respect to time reversal. As in the case of Boltzmann-Gibbs class statistics, the conclusion is based on the theory of equilibrium fluctuations of dynamic state parameters and on the property of invariance of fluctuations with respect to time inversion. The Onsager postulate is used, according to which the damping of equilibrium fluctuations of thermodynamic variables is described by linear differential equations of the first order. Traditional reciprocity relations for additive systems are obtained from the derived relations in the case when the deformation parameter q included in the parametric functional of the Tsallis entropy, is equal to unity.