Abstract
We consider the topic of symmetries as classifying tools for thermodynamic systems. We adopt the contact geometry approach, in a general framework including standard homogeneous thermodynamics but not limited to it, and we focus our attention on the problem of the existence of a general symmetry, to be defined as a symmetry which is the same for a class of thermodynamic systems. Homogeneity symmetry of standard equilibrium thermodynamics is the paradigmatic example of general symmetry, and we point out its being associated with a multi-class thermodynamics, whose mathematical characterization is taken into account. Furthermore, quasi-homogeneity symmetry, which describes some non-extensive systems, is shown to give rise to a general symmetry, in the above sense, in the case of non-relativistic self-gravitating fermions. In the latter case, it is also conjectured to give rise to a multi-class structure. An analysis of the behavior of transversal symmetries under the partial Legendre involutions enhances a special role of quasi-homogeneity symmetry, as well as the role of special thermodynamic limit is pointed out as a tool for investigating the topic of general symmetries.
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Belgiorno, F., Cacciatori, S.L. General symmetries: From homogeneous thermodynamics to black holes. Eur. Phys. J. Plus 126, 86 (2011). https://doi.org/10.1140/epjp/i2011-11086-8
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DOI: https://doi.org/10.1140/epjp/i2011-11086-8