Generalized Gibbs ensembles for time-dependent processes

Annals of Physics

Volumn 320, Issue 1, 2005, Pages 135-163

  Chomaz, Ph ^a   Gulminelli, F ^b   Juillet, O ^b  

^a GANIL   (France)

^b Laboratoire de Physique Corpusculaire   (France)

Author keywords

Flows; Information theory; Non equilibrium

Indexed keywords

EID: 27244444680     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2005.05.005     Document Type: Article

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32. For infinite systems the discussion is now focused mainly on the issue of non-extensivity, linked to the introduction of entropies different from the Shannon one [2], and to the study of systems with long range interactions [3].
33. When the system is finite the latter case deserves even more discussion since the factorization of the thermodynamics of the bath is not guaranteed out of the thermodynamic limit.
34. For an isolated system described by an hamiltonian H, the ergodic picture defines a unique microcanonical equilibrium characterized by all the conserved quantities, the energy and other observable related to the symmetries of H [8]. For a system in contact with a reservoir, we may get the different statistical ensembles depending on the conserved quantities characterizing the coupling with the bath
35. It should be noticed that in the Liouville space the measure is simply a projection 〈Â〉 = «A∥ρ»
36. Recall that if the unperturbed solution corresponds to a minimum in the energy surface and not to a maximum or to a saddle point, then the RPA eigenmodes are real [21]
37. Writing Eq. (40) we have implicitly assumed that the confining potential is known with an infinite accuracy. For realistic physical applications, the external potential should also be treated using information theory [15], and the statistical density matrix should be averaged over the distribution of k which minimizes the information (see Appendix B).
38. Depending upon the actual system studied, more observables describing its size or shape might be needed. Then, all those observables should be introduced as constraints in the minimization of the information to obtain an adequate statistical description.
39. 2) if the system is not spherical in average but has a finite quadrupole deformation