Title: Properties of a Majorana fermion ensemble with exciton-like mass

Abstract: Considering the relativistic scenario, we dedicate our study to the relativistic quantum description of one-dimensional Majorana fermions. Thus, we focus on aspects related to exciton-like particles. Seeking to reach our purpose, one analyzes the relativistic quantum mechanical system characterized by an effective mass distribution. In this context, we adopt an exciton-like position-dependent mass without impurity, i.e., without electromagnetic interactions. From this perspective, one notes results of noteworthy interest as consequences of the theory adopted. For instance, we highlight that, even without interaction, exciton-like Majorana fermions manifest theoretically bound states. Also, we construct a Majorana fermion ensemble with effective mass immersed in a thermal reservoir. That allows for a thorough investigation of the thermodynamic properties of the system. Among the thermodynamic characteristics studied in the canonical ensemble, we focus on the Helmholtz free energy, mean energy, entropy, and heat capacity. The numerical results obtained for these thermodynamic properties corroborate the validity of the Dulong-Petit law for our system.