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New approach to classical thermodynamics

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We easily get accustomed to uniformity and constancy and cease to observe it. The usual things become natural and understandable, while the unusual ones seem unnatural and incomprehensible. Essentially, we cannot understand, but can only grow accustomed.

Ya. Frenkel

Abstract

The author constructs a new conception of thermodynamics which is based on new results in number theory. We consider a maximally wide range of gases, liquids, and fluids to which, in principle, the Carathéodory approach can be applied. The Carathéodory principle is studied using the Lennard-Jones potential as an example. On the basis of this example, we analyze the dispersive structure of a fluidwhose density exceeds the critical value. We introduce a new parameter, the “jamming factor,” which determines the jamming effect for such fluids. A comparison with experimental data for nonpolar molecules is carried out. The phase transition “liquid-amorphous solid” is studied in detail in the domain of negative pressures. We discuss the theoretical relationship between the obtained solutions and econophysics, some mysteries in biology, and other sciences.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. P. Maslov

  2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    V. P. Maslov

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  1. V. P. Maslov
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Correspondence to V. P. Maslov.

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Maslov, V.P. New approach to classical thermodynamics. Math Notes 100, 154–185 (2016). https://doi.org/10.1134/S0001434616070142

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