Lorentz-violating scenarios in a thermal reservoir

In this work, we analyze the thermodynamic properties of the graviton and the generalized model involving anisotropic Podolsky and Lee$-$Wick terms with Lorentz violation. We build up the so-called partition function from the accessible states of the system seeking the following thermodynamic functions: spectral radiance, mean energy, Helmholtz free energy, entropy and heat capacity. Besides, we verify that, when the temperature rises, the spectral radiance $\chi(\nu)$ tends to attenuate for fixed values of $\xi$. Notably, when parameter $\eta_{2}$ increases, the spectral radiance $\bar{\chi}(\eta_{2},\nu)$ weakens until reaching a flat characteristic. Finally, for both theories, we perform the calculation of the modified black body radiation and the correction to the $\textit{Stefan-Boltzmann}$ law in the inflationary era of the universe.