2026/07/24 by Andreas Aste
Physics and Astronomy · #Statistical Mechanics and Entropy #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Non-Hermitian Physics
paper · doi:10.1088/1361-6552/ae8a03
Abstract A simple derivation of the entropy of the ideal and the dilute hard-sphere gas up to a normalization constant is presented, using only high school-level mathematics. The connection between information theory and thermodynamics, as well as the role of Heisenberg’s uncertainty principle in the transition from the classical to the quantum description of physical systems, is highlighted in a concise manner accessible to non-experts with a general interest in the natural sciences. A brief discussion is also devoted to the ultra-relativistic gas which can be analysed with the same elementary approach used for the non-relativistic case.