Summary
The problem of which transformations of variables leave thermodynamic laws invariant is considered. It is shown that contact transformations in the space of odd dimensionality spanned by all the fields and density variables together provide the solution of the classical problem. It is also shown that in this framework it is possible to give a consistent «derivation» of the Gibbs phase rule which avoids the introduction of the «metastable» extension of the one-phase equilibrium surfaces.
Riassunto
Si considera il problema di determinare quali trasformazioni di variabili lasciano invariate le leggi della termodinamica. Si mostra che le trasformazioni di contatto nello spazio di dimensionalità dispari descritto da tutti i «campi» e le densità forniscono la soluzione di questo classico problema. Si mostra inoltre che in questo schema è possibile dare una «derivazione» del tutto consistente, dal punto di vista termodinamico, della regola delle fasi di Gibbs, evitando l'introduzione dell'estensione «metastabile» delle superfici di equilibrio.
Резюме
Рассматривается проблема, какие преобразования переменных сохраняют законы термодинамнки инвариантными. Показывается, что контактные преобразования в пространстве нечетного числа измерений, которые охватывают все переменные полей и плотности, обеспечивают решение этой классической проблемы. Также показывается, что в этом подходе возможно дать полностью самосогласованный «вывод» правила фаз Гиббса, который позволяет избежать введения «метастабильного» продолжения однофазовых равновесных поверхностей.
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Mistura, L. Change of variables in thermodynamics. Nuov Cim B 51, 125–146 (1979). https://doi.org/10.1007/BF02743702
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DOI: https://doi.org/10.1007/BF02743702