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Review
. 2022 Nov 18;27(22):8017.
doi: 10.3390/molecules27228017.

Setting Boundaries for Statistical Mechanics

Affiliations
Review

Setting Boundaries for Statistical Mechanics

Bob Eisenberg. Molecules. .

Abstract

Statistical mechanics has grown without bounds in space. Statistical mechanics of noninteracting point particles in an unbounded perfect gas is widely used to describe liquids like concentrated salt solutions of life and electrochemical technology, including batteries. Liquids are filled with interacting molecules. A perfect gas is a poor model of a liquid. Statistical mechanics without spatial bounds is impossible as well as imperfect, if molecules interact as charged particles, as nearly all atoms do. The behavior of charged particles is not defined until boundary structures and values are defined because charges are governed by Maxwell's partial differential equations. Partial differential equations require boundary structures and conditions. Boundary conditions cannot be defined uniquely 'at infinity' because the limiting process that defines 'infinity' includes such a wide variety of structures and behaviors, from elongated ellipses to circles, from light waves that never decay, to dipolar fields that decay steeply, to Coulomb fields that hardly decay at all. Boundaries and boundary conditions needed to describe matter are not prominent in classical statistical mechanics. Statistical mechanics of bounded systems is described in the EnVarA system of variational mechanics developed by Chun Liu, more than anyone else. EnVarA treatment does not yet include Maxwell equations.

Keywords: EnVarA; Maxwell equations; boundary conditions; statistical mechanics; variational methods.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The need for electrodynamics, not just electrostatics, is emphasized by Feynman, in language that could hardly be more explicit. See volume 2 of [4].
Figure 2
Figure 2
Classical and Core Maxwell equations. J˜ describes the flux of mass with charge, after the usual dielectric term is subtracted from J. ρf describes the distribution of charge after the usual dielectric term is subtracted from ρ. The charge ρ describe all charges, however small, and all flux J (of charges with mass), however fast, brief, and transient. They include polarization phenomena in the properties of ρ and J whereas the classical equations use an oversimplified representation (see text) that describes the polarization of an idealized dielectric by its dielectric constant εr with the appropriately modified definitions of charge and flux, namely the free charge ρf and J˜.
Figure 3
Figure 3
The vacuum capacitor illustrates the equality of total current.

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This research received no external funding.

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