Thermodynamic Properties Of Anisotropic Fermi Gases In Confined Space

In this paper, we systemically study the systems in confined space, the anisotropic pressure property of ideal Fermi gas. We first introduce in detail the recent research progress home and abroad on small scale system both in theory and experiment, and then introduce two important work in statistical physics about the side effects of ideal gas giant potentials: one, based on M. Kac's famous mathematical work, obtains the equation of state for ideal gases in two-dimensional confined space with irregular boundaries; Another method is for systems whose energy spectra are known, performs the sum over all states in grand potentials directly, and obtains the equation of state exactly. Based on the research above, in different shapes container we study this anisotropy in a thermodynamic manner and find that the thermodynamic pressures usually depend on the form of deformations, and hence not equal to each other which is a natural representation of the anisotropic mechanical properties of a confined ideal gas. We also find that the boundary effects are much more significant than the statistical fluctuations under low-temperature and high-density conditions. Finally, we show that there is little difference between the boundary effects in 2D space and those in 3D space.