We investigate superconducting systems with the use of the phenomenological Landau's theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantites (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can practically be used in many cases to find such thermodynamical quantities at the critical point which are extremely difficult to measure under the assumption that the other ones are already known. We additionally perform a test of the two derived relations by using two-band microscopic model, describing superconducting systems. We calculate the specific heat, order parameter and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.

We show that the chemical potential exhibits small but distinct kinks at all critical temperatures as the evidence for phase transitions in the electronic system, structural phase transitions included. In the case of, at least, two kinds of interacting electrons average occupation numbers exhibit the same behavior. We consider phase transitions from ferromagnet to paramagnet (F-P), from superconductor to normal system (S-N) and we investigate phase transitions of reentrant type (R) using a generalization of the model investigated in Ref. [1].The Hamiltonian of the model (three hybridized bands) can be written in the following form (grand canonical ensemble): the index α numbers the bands (α = 1, 2, 3) and μ is the chemical potential. The Hamiltonian (1) describes the magnetic interaction (localized 4f-spins), three hybridized bands and magnetic interactions between band electrons and localized 4f-spins, as well as, the intersite Cooper pairs interaction. (cf. e.g. [2]) between conduction electrons. To calculate the chemical potential μ we use the constraint Σ α n() = n (n(α) = Σσ (n)), where n is the average number of electrons per *

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