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Journal of Physics A Mathematical and General

Comments on the paper by Coveney and Penrose 'On the validity of the Brussels formalism in statistical mechanics'

Claude D. George, Ilya Prigogine

Published Aug 7, 1993• 3 citations
Publisher

Abstract

For original paper see Coveney et. al. ibid., vol.25, p.4947 (1992). The previous authors state, in the introductory section of their paper that they are looking only at a 'small part' of the Brussels formalism. The title of their paper does not reflect this restriction and refers to the general validity of the Brussels formalism. The criticisms are focused on a few papers published about twenty years ago. However, even restricted to these papers, their claims do not apply. The present authors point out two major misrepresentations.

DOI
10.1088/0305-4470/26/15/038

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For original paper see Coveney et. al., ibid., vol.25, p.4947 (1992). George and Prigogine (ibid., vol.26, p.3905, 1993) interpret the authors previous paper as destructive criticism of the Brussels formalism. However they argue that their aim was to discover conditions under which this method might be supported by rigorous analysis and that their results give a set of sufficient conditions, admittedly quite restrictive, for the validity of a part of the formalism. The Brussels school has never promulgated any agreed choice for the function space in which the formalism's operators are to act. In their work they chose a Hilbert space. This structure sufficed for the theorems they could prove, which concern only the P subspace. They agree that additional structure, such as that of a rigged Hilbert space, may be necessary to give effect to the Brussels formalism outside the P subspace, but since this additional structure would not have affected their results they do not see that its omission was a misrepresentation. Further comments are made.

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For original paper see Coveney et. al. ibid., vol.25, p.4947 (1992). The previous authors state, in the introductory section of their paper that they are looking only at a 'small part' of the Brussels formalism. The title of their paper does not reflect this restriction and refers to the general validity of the Brussels formalism. The criticisms are focused on a few papers published about twenty years ago. However, even restricted to these papers, their claims do not apply. The present authors point out two major misrepresentations.
For original paper see Coveney et. al., ibid., vol.25, p.4947 (1992). George and Prigogine (ibid., vol.26, p.3905, 1993) interpret the authors previous paper as destructive criticism of the Brussels formalism. However they argue that their aim was to discover conditions under which this method might be supported by rigorous analysis and that their results give a set of sufficient conditions, admittedly quite restrictive, for the validity of a part of the formalism. The Brussels school has never promulgated any agreed choice for the function space in which the formalism's operators are to act. In their work they chose a Hilbert space. This structure sufficed for the theorems they could prove, which concern only the P subspace. They agree that additional structure, such as that of a rigged Hilbert space, may be necessary to give effect to the Brussels formalism outside the P subspace, but since this additional structure would not have affected their results they do not see that its omission was a misrepresentation. Further comments are made.
For the original article see ibid., vol.40, no.5, p.820-6 (1992). The commenter points out that, in the above-titled paper by M.J. Wengler et al., no references published prior to 1982 are cited. As a result, no mention is made of a considerable body of relevant published work. The commenter discusses some of this earlier work. One of the authors, M.J. Wengler, replies that the earlier work all used point contact junctions with low capacitance and with nonhysteretic current-voltage (I-V) curves which fit the resistively shunted Josephson junction (RSJ) circuit model, whereas he and his coauthors considered planar SIS diodes with higher capacitance and with completely hysteretic I-Vs which are not even similar to the RSJ model predictions. He offers some further discussion of the ways in which their results are distinct from the earlier work.>