Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió publicadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/53290
Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.
Matèries
Matèries (anglès)
Citació
Citació
LATELLA, Ivan, PÉREZ MADRID, Agustín. Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions. _Physical Review E_. 2013. Vol. 88, núm. 4, pàgs. 042135-1-042135-11. [consulta: 21 de gener de 2026]. ISSN: 1539-3755. [Disponible a: https://hdl.handle.net/2445/53290]