Pathological limits in statistical mechanics
C. Y. Chen
TL;DR
This paper critically examines the mathematical validity of certain limit-like quantities in statistical mechanics and proposes that redefining these quantities can lead to advances in non-equilibrium gas dynamics.
Contribution
It identifies ill-defined limit-like quantities in statistical mechanics and suggests new formulations to improve understanding of non-equilibrium gas behavior.
Findings
Some limit-like quantities are mathematically ill-defined.
Redefining these quantities can advance non-equilibrium gas dynamics.
New formulations improve theoretical understanding.
Abstract
This paper shows that some of the limit-like quantities currently used in statistical mechanics are ill-defined in the mathematical sense. Along the line, it is shown that significant progresses in non-equilibrium gas dynamics can be made by redefining, reinterpreting, and reformulating those quantities.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Statistical Mechanics and Entropy · Quantum Mechanics and Applications