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Updated: Jan 20, 2026
Third Law of Thermodynamics and Standard Molar Entropy
Dimensional ensemble and (topological) fracton thermodynamics: the slow route to equilibrium
1Departamento de Física, FACI, Universidad de Tarapacá, Casilla 7-D, Arica, Chile. cflores@uta.cl.
Abstract:
The use of the dimensional-ensemble becomes compulsory when spatial dimensions are not well defined. Consequently, apart from temperature, thermodynamic equilibrium requires an additional configurational parameter. Two representative cases are considered in detail: oscillators with undefined spatial dimension and topological fractons. Spatial dimension and energy are determined as a function of temperature in both cases. At low temperatures, specific heat behaves exponentially, meaning it creates a slow route to equilibrium. In accordance with experiments, calculations suggest that the spatial dimension diminishes when temperature decreases. Parameter values are computed using data obtained from almost two-dimensional graphene and porous compounds.
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