Entropy Analysis of Implicit Heat Fluxes in Multi-Temperature Mixtures.

We propose new implicit constitutive relations for the heat fluxes of a two-temperature mixture of fluids. These relations are frame-indifferent forms. However, classical explicit forms of the stress tensors and the interaction forces (specified as explicit forms of constitutive relations) as given in mixture theory are used. The focus here is to establish constraints imposed on the implicit terms in the heat fluxes due to the Second Law of Thermodynamics. Our analysis establishes that the magnitude of the explicit entropy production is equal to or greater than that of the implicit entropy production.

Visualizing genomic data: The mixing perspective.

We report on a novel way to visualize genomic data. By considering genome coding sequences, cds, as sets of the N=61 non-stop codons, one obtains a partition of the total number of codons in each cds. Partitions exhibit a statistical property known as mixing character which characterizes how mixed the partition is. Mixing characters have been shown mathematically to exhibit a partial order known as majorization (Ruch, 1975). In previous work (Seitz and Kirwan, 2022) we developed an approach that combined mixing and entropy that is visualized as a scatter plot. If we consider all 1,121,505 partitions of 61 codons, this produces a plot we call the theoretical mixing space, TGMS. A normalization procedure is developed here and applied to real genomic data to produce the genome mixing signature, GMS. Example GMS's of 19 species, including Homo sapiens, are shown and discussed.

Mixed-Up-Ness or Entropy?

Mixed-up-ness can be traced to unpublished notes by Josiah Gibbs. Subsequently, the concept was developed independently, and under somewhat different names, by other investigators. The central idea of mixed-up-ness is that systems states can be organized in a hierarchy by their degree of mixed-up-ness. In its purest form, the organizing principle is independent of thermodynamic and statistical mechanics principles, nor does it imply irreversibility. Yet, Gibbs and subsequent investigators kept entropy as the essential concept in determining system evolution, thus retaining the notion that systems evolve from states of perfect "order" to states of total "disorder". Nevertheless, increasing mixed-up-ness is consistent with increasing entropy; however, there is no unique one-to-one connection between the two. We illustrate the notion of mixed-up-ness with an application to the permutation function of integer partitions and then formalize the notion of mixed-up-ness as a fundamental hierarchal principle, the law of mixed-up-ness (LOM), for non-thermodynamic systems.

Ocean convergence and the dispersion of flotsam.

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change. Although this paradigm is likely valid at mesoscales, larger than 100 km in horizontal scale, recent theoretical studies of submesoscales (less than ∼10 km) predict strong surface convergences and downwelling associated with horizontal density fronts and cyclonic vortices. Here we show that such structures can dramatically concentrate floating material. More than half of an array of ∼200 surface drifters covering ∼20 × 20 km2 converged into a 60 × 60 m region within a week, a factor of more than 105 decrease in area, before slowly dispersing. As predicted, the convergence occurred at density fronts and with cyclonic vorticity. A zipperlike structure may play an important role. Cyclonic vorticity and vertical velocity reached 0.001 s-1 and 0.01 ms-1, respectively, which is much larger than usually inferred. This suggests a paradigm in which nearby objects form submesoscale clusters, and these clusters then spread apart. Together, these effects set both the overall extent and the finescale texture of a patch of floating material. Material concentrated at submesoscale convergences can create unique communities of organisms, amplify impacts of toxic material, and create opportunities to more efficiently recover such material.