  Exact and approximate expressions for thermodynamic characteristics of heated
matter, which consists of particles with finite mass-widths, are constructed.
They are expressed in terms of Fermi/Bose distributions and spectral functions,
rather than in terms of more complicated combinations between real and
imaginary parts of the self-energies of different particle species. Therefore
thermodynamically consistent approximate treatment of systems of particles with
finite mass-widths can be performed, provided spectral functions of particle
species are known. Approximation of the free resonance gas at low densities is
studied. Simple ansatz for the energy dependence of the spectral function is
suggested that allows to fulfill thermodynamical consistency conditions. On
examples it is shown that a simple description of dense systems of interacting
particle species can be constructed, provided some species can be treated in
the quasiparticle approximation and others as particles with widths. The
interaction affects quasiparticle contributions, whereas particles with widths
can be treated as free. Example is considered of a hot gas of heavy fermions
strongly interacting with light bosons, both species with zero chemical
potentials. The density of blurred fermions is dramatically increased for high
temperatures compared to the standard Boltzmann value. The system consists of
boson quasiparticles (with effective masses) interacting with fermion --
antifermion blurs. In thermodynamical values interaction terms partially
compensate each other. Thereby, in case of a very strong coupling between
species thermodynamical quantities of the system, like the energy, pressure and
entropy, prove to be such as for the quasi-ideal gas mixture of quasi-free
fermion blurs and quasi-free bosons.
