Impact of the Sagnac Effect on Thermodynamic and Magnetocaloric Properties of a Rotating Two-Dimensional Electron Gas

This work investigates the impact of the Sagnac effect on the thermodynamic properties of a non-interacting two-dimensional electron gas (2DEG) in a rotating sample under the influence of a uniform magnetic field. We derive an analytical expression for the energy spectrum using an effective Hamiltonian that incorporates inertial forces, and then apply canonical ensemble statistical mechanics to evaluate thermodynamic quantities. The results show that rotation modifies the energy levels, the application of a magnetic field leads to the formation of Landau levels further altered by rotation and gravitational mass, and thermodynamic quantities (internal energy, specific heat, free energy, entropy, magnetization, and magnetocaloric effect) exhibit a strong dependence on these parameters. In particular, the difference between effective mass $m^*$ and gravitational mass $m_G$ influences magnetization and the magnetocaloric effect, with negative rotations potentially inducing a cooling effect when these masses are distinct. We conclude that rotational effects and effective mass properties are crucial for understanding the thermodynamics of electronic systems under magnetic fields, with implications for thermal modulation in semiconductor materials.