The role of curvature in quantum statistical mechanics
Marcelo R. Ubriaco
TL;DR
This paper investigates how the scalar curvature of a thermodynamic space reveals stability and exotic behaviors in quantum systems, including anyonic statistics and fractal distributions.
Contribution
It introduces a method to analyze quantum systems' stability and properties via scalar curvature in thermodynamic geometry, focusing on quantum group invariance and fractal distributions.
Findings
Scalar curvature indicates stability regions in quantum thermodynamic systems.
Identification of potential anyonic behavior through geometric analysis.
Insights into systems with fractal distribution functions.
Abstract
In this manuscript, we calculate the scalar curvature of a two-dimensional thermodynamic space to study the properties of two thermodynamic systems. In particular, we study the stability and possible anyonic behavior of quantum group invariant systems and systems with fractal distribution functions.
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Taxonomy
Topicsadvanced mathematical theories · Black Holes and Theoretical Physics · Nonlinear Waves and Solitons