Eur. Phys. J. C (2017) 77: 158
https://doi.org/10.1140/epjc/s10052-017-4739-3

Regular Article - Theoretical Physics

Homogeneity and thermodynamic identities in geometrothermodynamics

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, AP 70543, 04510, Mexico, DF, Mexico
² Dipartimento di Fisica and ICRANet, Università di Roma “La Sapienza”, 00185, Rome, Italy
³ Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad Militar Nueva Granada, Cra 11 No. 101-80, Bogotá D.E., Colombia
⁴ Departamento de Posgrado, CIIDET, AP752, 76000, Querétaro, QRO, Mexico

^* e-mail: quevedo@nucleares.unam.mx

Received: 24 January 2017
Accepted: 6 March 2017
Published online: 14 March 2017

Abstract

We propose a classification of thermodynamic systems in terms of the homogeneity properties of their fundamental equations. Ordinary systems correspond to homogeneous functions and non-ordinary systems are given by generalized homogeneous functions. This affects the explicit form of the Gibbs–Duhem relation and Euler’s identity. We show that these generalized relations can be implemented in the formalism of black hole geometrothermodynamics in order to completely fix the arbitrariness present in Legendre invariant metrics.