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

Abstract

The Comments are explicitly related to contents of two published papers: actual [1] and [2]. A third paper [3], where the measured screening potential liquid-solid difference is explained using the correlation entropy S − , should also be considered.The mechanism described in the published paper [1] that increases the kinetic energy of light nuclei undergoing nuclear fusion, usually low energy deuterons accelerated against a host environment with implanted deuterons, does not substitute the electronic screening mechanism (as the standard Salpeter screening, the adiabatic or other proposed stationary or dynamic versions). It must be taken in addition to the electron screening potential energy after the stopping power corrections as, for instance, in the case of d-d fusion in deuterated metals or other similar fusion reactions.The contributions of the positive and negative parts of entropy of the environment, given in [1], concern the entropy per single ion (S + and S − are in k B units per ion). The negative part (negentropy), is related to many-body correlations. To explain experimental results we require that the number of ions involved in the mechanism contributing to the enhancement of the fusion rates is of the order of few thousands depending on the fusion reaction and on the host environment. This amount of ions, compared to the Avogadro number, is almost negligible. The ions contributing are those belonging to the cage (Ref.[57] of [1], p. 655; see also Verlet and Weis [4]) of the fusing ions during their mean free path between two elastic collisions. Consequently, total S + and S − of the complete host environment are not modified, the mechanical and thermodynamic bulk properties of the host environment are not changed at all. The environment does not relax or make transitions to a different thermodynamic state, remains stable with its entropy sum of positive and negative contributions. The parameters characteristic of the environment can fluctuate around their mean values.The choice to write the entropy as the sum of two contributions (available for work, unavailable) already indicated by Clausius (valoric interpretation of entropy [5]) and used, for instance, by Klimontovich [6,7] and by Chang (Refs. [16,17] of [1]), in many works when the system is away from the q = 1 global equilibrium state, permits to take track of the rôle of the two parts. Entropy can be thought in terms of distance from equilibrium and of relative phase space occupation instead of measure of disorder.In the lack of direct measurements of distribution functions, Wallace (Refs.

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