Comments on Piero Quarati et al. Negentropy in Many-Body Quantum Systems. Entropy 2016, 18, 63

The purpose of this note is to express my concerns about the published paper by Quarati et al. (Entropy 2016, 18, 63). It is hoped that these comments will stimulate a constructive discussion of the issues involved. The above paper by Quarati et al. [1] argues that the concept of negentropy can be useful in understanding the observed enhancements of nuclear fusion rates in the solar plasma and in liquid metals with respect to standard Saltpeter screening in the solar plasma case, and in a liquid metal host as compared with the solid host. It is argued that the host systems possess a certain level of organization, expressed in terms of negentropy, that is available for transferral to the fusing nuclei to enhance their fusion rates. The definition of negentropy is provided in the first sentence, “Negative entropy, or negentropy [1–3] (Refs. in [1]), can be defined as the specific entropy deficit of an ordered subsystem with respect to surrounding chaos.” The concept is elaborated at a number of points later (first at the end of the fourth paragraph) as “stored mobilizable energy in an organized system ... which can be spontaneously transferred or exchanged among the elements or clusters of elements or from environment to elements and subsystems.” Exploring the use of negentropy to better understand purely physical phenomena is an attractive idea, for its success in this arena is bound to have implications for its use in complex chemical and biological systems. While the definition of negentropy may be necessarily vague, as with many other subtle scientific concepts, one would hope that in a simpler physical system, a more precise definition of negentropy could be fleshed out, and the detailed mechanism for entropy or free energy transfer described and worked out. In this work a sharper definition leading to numerical estimates is sought, while the detailed mechanism is left for future work. My concern in this case is that the sharper definition, or “operational definition” corresponding to what is actually calculated, is inconsistent with the definition given above. Briefly stated, the equilibrium entropy of the medium consists of a number of terms, at least one of which contributes negatively. Such a negative term (or terms) are identified as negentropy. This is first stated at the beginning of the fourth paragraph of the introduction and made more explicit through examples in later sections. The negative contributions come from interactions which produce correlations in the ions of the metal or in the solar plasma, or from quantum degeneracy of the conduction electrons in metals. These contributions are identified explicitly by equations in the text: For liquid metals, by Equations (16) and (19) (equations derived by Wallace [2]); for the solar plasma, by Equation (24) (written in terms of the free energy as in Ref. [59] of [1]). In solid metals, the analogous terms are small compared with the above, but they provide instructive textbook examples of equilibrium entropies: The ionic lattice contribution is found in Equation (6). The conduction electron contribution (Equations (10) and (13)) is due to quantum degeneracy, and makes a similar small contribution in both solid and liquid metals. Entropy 2016, 18, 125; doi:10.3390/e18040125 www.mdpi.com/journal/entropy Entropy 2016, 18, 125 2 of 3 The problem with the above operational definition is that the total entropy expressions of which these negative contributions are a part describe systems in equilibrium (not metastable equilibrium, as argued in Section II—see below). Such a contribution (representing correlations or quantum degeneracy) cannot represent a “specific entropy deficit” as in the initial definition; or a “stored mobilizable energy” (or free energy) available for spontaneous transferral to the fusing nuclei. Put another way, there are no thermodynamic states into which these systems, so described, can relax spontaneously with the release of free energy. The initial draft of these comments ended here, with the belief that the argument is complete. However, this would not have been fair to the readers or to the authors. The authors’ arguments are grounded in earlier work, and they deserve further discussion. The arguments leading to the above operational definition are given in Section II. The total entropy is written there as the sum,