Work

Scaling Symmetry in Symplectic Thermodynamics

Year: 2026

Type: article

Abstract: This paper investigates scaling symmetry in thermodynamics by unifying constrained Hamiltonian dynamics with symplectic and contact geometries. Through the mathematical processes of contactization and symplectization, we demonstrate that fixing an extended global scale variable effectively recovers the standard thermodynamic description in terms of scale-invariant quantities. The geometric formalism is illustrated by establishing the diffeomorphism between the Lagrangian submanifolds of ideal and van der Waals gases. Finally, applying this framework to a Schwarzschild black hole reveals that changing the scaling weights of entropy and internal energy is a fundamental physical requirement to accommodate non-isothermal dynamics.

Source: Symmetry

DOI: 10.3390/sym18071110

Authors: Mario C. Baldiotti, Rodrigo Fresneda

Institutions: Universidade Estadual de Londrina, Universidade Federal do ABC

Language: English

Topic: Advanced Thermodynamics and Statistical Mechanics

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Fundação de Amparo à Pesquisa do Estado de São Paulo