In the present work the thermodynamical properties of bosonic and fermionic gases are analyzed under the condition that a modified dispersion relation is present. This last condition implies a breakdown of Lorentz symmetry. The implications upon the condensation temperature will be studied, as well, as upon other thermodynamical variables such as specific heat, entropy, etc. Moreover, it will be argued that those cases entailing a violation of time reversal symmetry of the motion equations could lead to problems with the concept of entropy. Concerning the fermionic case it will be shown that Fermi temperature suffers a modification due to the breakdown of Lorentz symmetry. The results will be applied to white dwarfs and the consequences upon the Chandrasekhar mass–radius relation will be shown. The possibility of resorting to white dwarfs for the testing of modified dispersion relations is also addressed. It will be shown that the comparison of the current observations against the predictions of our model allows us to discard some values of one of the parameters appearing in the modifications of the dispersion relation.