1. A. Einstein, Annalen der Physik 33, 1275 (1910) [ “Usually W is put equal to the number of complexions... In order to calculate W, one needs a complete (molecular-mechanical) theory of the system under consideration. Therefore it is dubious whether the Boltzmann principle has any meaning without a complete molecular-mechanical theory or some other theory which describes the elementary processes. $S=\frac{R}{\cal N}\log W+\;{\rm const}$ . seems without content, from a phenomenological point of view, without giving in addition such an Elementartheorie.” (Translation from Abraham Pais, Subtle is the Lord..., Oxford University Press, 1982)]
2. K. Huang, Statistical Mechanics (J. Wiley and Sons, New York, 1987), pp. 90–91 [ “We mentioned the ergodic theorem in Section 3.4, but did not use it as a basis for the microcanonical ensemble, even though, on the surface, it seems to be the justification we need. The reason is that existing proofs of the theorem all share (...) an avoidance of dynamics. For this reason, they cannot provide the true relaxation time for a system to reach local equilibrium (typically about 10-15 s for real systems), but have a characteristic time scale of the order of the Poincaré cycle. For this reason, the ergodic theorem has so far been an interesting mathematical exercise irrelevant to physics.”]
3. F. Takens, in Structures in dynamics — Finite dimensional deterministic studies, edited by H.W. Broer, F. Dumortier, S.J. van Strien, F. Takens (North-Holland, Amsterdam, 1991), p. 253 [ “The values of pi are determined by the following dogma: if the energy of the system in the ith state is Ei and if the temperature of the system is T then: $p_i=\exp\{-E_i/kT\}/Z(T)$ , where $Z(T)=\sum_i \exp\{-E_i/kT\}$ , (this last constant is taken so that $\sum_i p_i=1$ ). This choice of pi is called Gibbs distribution. We shall give no justification for this dogma; even a physicist like Ruelle disposes of this question as “deep and incompletely clarified."]
4. M.C. Carotta, C. Ferrario, G. Lo Vecchio, L. Galgani, Phys. Rev. A 17, 786 (1978); see also, A. Carati, L. Galgani, B. Pozzi, Phys. Rev. Lett. 90, 010601 (2004)
5. R. Livi, M. Pettini, S. Ruffo, A. Vulpiani, J. Stat. Phys. 48, 539 (1987); C. Giardinà, R. Livi, J. Stat. Phys. 91, 1027 (1998); see also D. Escande, H. Kantz, R. Livi, S. Ruffo, J. Stat. Phys. 76, 605 (1994)