2023/03/24 by Mário J. Pinheiro, Pinheiro, Mario J.
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #General Physics (physics.gen-ph) #Phase Equilibria and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2303.16077
openalex publication_date 2023/03/24 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28
The Liouville theorem is a fundamental concept in understanding the properties of systems that adhere to Hamilton's equations. However, the traditional notion of the theorem may not always apply. Specifically, when the entropy gradient in phase space fails to reach equilibrium, the phase-space density may not have a zero time derivative, i.e., (dρ)/(dt) may not be zero. This leads to the concept of the set of attainable states of a system forming a compressible "fluid" in phase space. This observation provides additional insights into Hamiltonian dynamics and suggests further examination in the fields of statistical physics and fluid dynamics. In fact, this finding sheds light on the limitations of the Liouville theorem and has practical applications in fields such as beam stacking, stochastic cooling, and Rabi oscillations, among others.