In this paper, a point of view is assumed where the tokamak is treated as a thermodynamic system open to external interactions. Those stationary states of the plasma are considered that are associated with a stationary entropy, i.e. with equilibrium between the entropy produced by the plasma and the entropy injected into it through the auxiliary heating. By means of the concept of magnetic entropy (a quantity that measures, in the framework of information theory and under suitable constraints, the probability of coarse-grained current density configurations), the responses can be analysed of the equilibrium magnetic configuration and of the related pressure profile to the intensity and to the deposition profile of the auxiliary heating when a condition of stationary entropy is attained. These factors are found to have considerable bearings on the magnetic equilibrium – in particular on the generation of states with negative magnetic shear. Moreover, the existence of a thermodynamic relation between entropy production and thermal conductivity involves a connection between magnetic structure and transport properties, and implies a strong reduction of the heat flow in the region of low or negative shear. Examples of practical interest are discussed both in the case of a homogeneous and that of a sharply localized power deposition.