  A deformed fermion gas model aimed at taking into account thermal and
electronic properties of quasiparticle systems is devised. The model is
constructed by the fermionic Fibonacci oscillators whose spectrum is given by a
generalized Fibonacci sequence. We first introduce some new properties
concerning the Fibonacci calculus. We then investigate the low-temperature
thermostatistical properties of the model, and derive many of the deformed
thermostatistical functions such as the chemical potential and the entropy in
terms of the model deformation parameters p and q. We specifically focus on the
p,q-deformed Sommerfeld parameter for the heat capacity of the model, and its
behavior is compared with those of both the free-electron Fermi theory and the
experimental data for some materials. The results obtained in this study reveal
that the present deformed fermion model leads to an effective approach
accounting for interaction and compositeness of quasiparticles, which have
remarkable implications in many technological applications such as in
nanomaterials.
