A Thermodynamic Classification of Real Numbers
Thomas Garrity
TL;DR
This paper introduces a novel classification system for real numbers inspired by statistical mechanics, focusing on the Diophantine properties of their continued fraction expansions to better understand their mathematical nature.
Contribution
It presents a new classification scheme for real numbers based on thermodynamic ideas and Diophantine properties, extending previous work by Knauf and Fiala and Kleban.
Findings
Classification scheme links thermodynamics with number theory
Highlights the role of continued fraction properties in classification
Provides a framework for analyzing real numbers through statistical mechanics
Abstract
A new classification scheme for real numbers is given, motivated by ideas from statistical mechanics in general and work of Knauf and of Fiala and Kleban in particular. Critical for this classification of a real number will be the Diophantine properties of its continued fraction expansion.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Theories and Applications · Mathematical and Theoretical Analysis