Scaling symmetry is incorporated into thermodynamics via symplectic and contact geometries, yielding a diffeomorphism between ideal and van der Waals gas submanifolds and showing that scale symmetry between energy and entropy must break for non-isothermal Schwarzschild black hole dynamics.
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Scaling Symmetry in Symplectic Thermodynamics
Scaling symmetry is incorporated into thermodynamics via symplectic and contact geometries, yielding a diffeomorphism between ideal and van der Waals gas submanifolds and showing that scale symmetry between energy and entropy must break for non-isothermal Schwarzschild black hole dynamics.