Disentangling Thermal and Degeneracy Pressure in Quantum-Confined Fermi Gases

A theoretical framework is developed to decompose the total pressure of a quantum-confined Fermi gas into degeneracy pressure, arising from Fermi–Dirac statistics, and thermal pressure, associated with finite-temperature excitations. Using Weyl’s conjecture for the confined density of states, geometric confinement effects are incorporated through surface-and edge-to-volume parameters (α and β). Exact analytical expressions for both components are derived using polylogarithmic functions, and asymptotic forms are obtained for the strongly degenerate (T ≪ T_F) and weakly degenerate (T ≫ T_F) regimes. The analysis shows that quantum confinement enhances degeneracy pressure by a factor of (1 + 5α_F⁄16), while suppressing thermal pressure, with the contrast most significant under strong degeneracy. The maximum relative error in the total pressure, occurring at the crossover temperature T̃^∗~0.604282, is about 22%, while that for thermal pressure reaches 52%. The asymptotic expressions remain valid across α_F ∈ [0.1, 0.5] and β_F ∈ [0.01, 0.2]. Separating thermal and degeneracy contributions enables improved interpretation of thermodynamic measurements in confined quantum systems where only total pressure is accessible. The framework is relevant for nanoelectronic devices, ultracold atomic gases, and quantum dots, offering insight into how spatial confinement differentially shapes thermal and quantum contributions to observable thermodynamic behavior.