Talk:Density Expansions of Transport Coefficients for Gases

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    Reviewer A

    The review article “Density Expansions of Transport Coefficients for Gases” by Dorfman is accurate, well-written, and should be understandable by a broad audience interested in modern kinetic theory. Dorfman was one of the discoverers of the divergences in formal virial expansions for dynamical properties, and hence has historical perspective as well as detailed understanding of the mechanisms responsible for these divergences. The article is suitable for acceptance in its present form. However, my suggestions for possible improvement of the manuscript are the following: 1) Reference is made in the text to specific results or authors that are not part of the recommended references at the end. Assistance to the reader might be given by giving the authors and the date of the work cited. 2) The divergences of the density expansion for the transport coefficient can be considered as the combined density expansion for finite time phenomena with secular coefficients. However, the density expansions could be useful for predicting short time behavior properties such as time correlation functions. 3) The rearrangement of the divergent virial expansion by resummation of most divergent terms at all orders, exposes the physics of “collisional damping” on times of the order of the mean free time. This also suggests the basis for the more general ring kinetic theory, subsuming both the logarithmic components of the density expansions and the mode coupling effects for time dependent properties. Some further elaboration of the connection between the two might be helpful. 4) Small parameter expansions are appropriately formulated in a dimensionless representation. The present discussion corresponds to a length scale of the hard sphere diameter, and the time scale of the collision time. In these units the BBGKY has a single small parameter of n(sigma)3. A formal expansion of the solution to the hierarchy leads to the virial results described here. In hindsight, a different dimensionless formulation can be given using the mean free path and mean free time as characteristic length and time scales. The resulting dimensionless BBGKY hierarchy has a single small parameter sigma/mean free path, also proportional to of n(sigma)3 but appearing in a different location. The formal expansion of the solution to this hierarchy leads to the ring kinetic theory as the first correction to Boltzmann, clarifying the relevance of the most divergent resummation for the original virial expansion.

    Reviewer B

    Reviewer B: The paper is a clear introduction to the complex theme of the non-equilibrium virial expansion, its failure and the birth of the logarithmic corrections and long time tails. Aside from very minor typographic corrections ($t..$ $\to$ $t.$ on line 14 of the section "Formal, non-equilibrium virial expansions", and the broken line 7 in the section "Divergences in the virial expansion of the transport coefficients" due to the figure insertion) I would be pleased if the reference mentioned in the text were linked to the bibliography at the end of the article. Such a link (possibly enriched by the indication of the page or chapter where the statements can be found by an "unexperienced reader", in the style of bibtex for instance) will be extremely useful.

    Aside from the references link the evaluation of the present work is "excellent". In principle linking the references could be done by the editors: however I strongly recommend it to be done by the Author, to profit from his deep knowledge of a subject to which he has so much contributed.

    Suggestions for future developments: in section "Formal, non-equilibrium virial expansions" the Husimi expansion is mentioned: I would suggest the editors ask Professor Dorfman to propose an Author for such an entry (unless he himself may be willing to do so). Another topic that could be expanded in a future entry is a technical presentation of the last two paragraphs of the same section.

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