Gravitational Thermodynamics for Interstellar Gas and Weakly Degenerate Quantum Gas

• Published in: Journal of the Physical Society of Japan 2016-03, Vol.85 (3), p.1-1
• Main Authors: Zhu, Ding Yu, Shen, Jian Qi
• Format: Article
• Language: English
• Subjects: Density distribution; Entropy; Gases; Gravitation; Gravitational fields; Gravity; Ideal gas; Inhomogeneity; Quantum physics; Temperature distribution; Temperature gradient; Thermodynamics
• ISSN: 0031-9015; 1347-4073

The temperature distribution of an ideal gas in gravitational fields has been identified as a longstanding problem in thermodynamics and statistical physics. According to the principle of entropy increase (i.e., the principle of maximum entropy), we apply a variational principle to the thermodynamical entropy functional of an ideal gas and establish a relationship between temperature gradient and gravitational field strength. As an illustrative example, the temperature and density distributions of an ideal gas in two simple but typical gravitational fields (i.e., a uniform gravitational field and an inverse-square gravitational field) are considered on the basis of entropic and hydrostatic equilibrium conditions. The effect of temperature inhomogeneity in gravitational fields is also addressed for a weakly degenerate quantum gas (e.g., Fermi and Bose gas). The present gravitational thermodynamics of a gas would have potential applications in quantum fluids, e.g., Bose-Einstein condensates in Earth's gravitational field and the temperature fluctuation spectrum in cosmic microwave background radiation.