Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics

In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical points or real gases, whereas the jumps of critical indices and the Maxwell rule are related to the tunnel generalization of thermodynamics. Semiclassical methods are considered for the tunnel generalization of thermodynamics and also for the second and ultrasecond quantization (operators of creation and annihilation of pairs). To every pure gas there corresponds a new critical point of the limit negative pressure below which the liquid passes to a dispersed state (a foam). Relations for critical points of a homogeneous mixture of pure gases are given in dependence on the concentration of gases.Comment: 37 pages, 9 figure, more precise explanations, more references. arXiv admin note: substantial text overlap with arXiv:1202.525

Gas metasomatism: Experiments on natural Fumaroles of Kudryavyi Volcano, Iturup, Kuril Islands

Direct experiments on high-temperature (910 and 620°C) fumaroles of Kudryavy Volcano have demonstrated that low-density volcanic gas interacts with rock-forming and ore minerals (12 minerals were studied). The mechanism of the interaction is determined by gas metasomatism reactions: (a) at given conditions, sphalerite, calcite, barite, and gypsum are either dissolved and removed by gas or replaced with other minerals (calcite → anhydrite); (b) reactions with silicates (feldspars, olivine, and biotite) proceed owing to diffusion cation exchange. Structural rearrangements in biotite are possible due to dehydration and loss of alkalis and aluminum. The kinetics of interaction between hot gas and silicates is governed by the rate of cation diffusion in the mineral at given conditions. Precipitation of sublimates on the surfaces of minerals does not affect much the process of reactions. Interaction between volcanic gas and minerals results in albitization of feldspars and ferruginization of olivine and biotite. The scale of metasomatism in the crystalline rocks of Kudryavyi Volcano has been estimated as about 3 mm in 115 years

Discovery of a pure rhenium mineral at Kudriavy volcano

KUDRIAVY volcano on Iturup island in the Kuril arc is an active calc-alkaline volcano. It has not erupted this century; its current volcanic activity is characterized by hot (up to 910oC) gas jets which have been stable for at least 30 years. The composition of the gaseous emissions is typical of high-temperature fumaroles, but we report here the discovery of unusual subsurface sublimates associated with one gas jet—a sulphide mineral containing rhenium as the only cation. To our knowledge, this is the first reported occurrence of a pure rhenium mineral. The concentration of rhen-ium in the fumarole gas is only 2–10 p.p.b., so the condensation of pure rhenium sulphide from this gas requires both enrichment of rhenium by eight orders of magnitude and remarkable selectivity. Rhenium is generally believed to exist in only trace amounts at the Earth's surface, but our findings demonstrate that it can be readily mobilized, dispersed and concentrated by degassing magmas