Dilational Symmetry-Breaking in Thermodynamics

Abstract

Using thermodynamic relations and dimensional analysis we derive a general formula for the thermodynamical trace $2\mathcal{E}-DP$ for non-relativistic systems and $\mathcal{E}-\mathcal{DP}$ for relativistic systems, where $D$ is the number of spatial dimensions, in terms of the microscopic scales of the system within the grand canonical ensemble. We demonstrate the formula for several cases, including anomalous systems which develop scales through dimensional transmutation. Using this relation, we make explicit the connection between dimensional analysis and the virial theorem. This paper is focused mainly on the non-relativistic aspects of this relation.

10 pages (this version is the published version)

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Cited by in corpus (3)

• Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
• Virial theorem, boundary conditions, and pressure for massless Dirac electrons