Mathematical Structure Of Thermodynamics Research Articles

Thermodynamical Arguments Against Evolution

The argument that the second law of thermodynamics contradicts the theory of evolution has recently been revived by anti-evolutionists. In its basic form, the argument asserts that whereas evolution implies that there has been an increase in biological complexity over time, the second law, a fundamental principle of physics, shows this to be impossible. Scientists have responded primarily by noting that the second law does not rule out increases in complexity in open systems, and since the Earth receives energy from the Sun, it is an open system. This reply is correct as far as it goes, and it adequately rebuts the most crude versions of the second law argument. However, it is insufficient against more sophisticated versions, and it leaves many relevant aspects of thermodynamics unexplained. We shall consider the history of the argument, explain the nuances various anti-evolution writers have brought to it, and offer thorough explanations for why the argument is fallacious. We shall emphasize in particular that the second law is best viewed as a mathematical statement. Since anti-evolutionists never make use of the mathematical structure of thermodynamics, invocations of the second law never contribute anything substantive to their discourse.

Reply to: “Additional remarks related with the discussion inaugurated by the article ‘Incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics’ by D. J. Bottomley et al. [Surf. Sci. 603 (2009) 97

Reply to: “Additional remarks related with the discussion inaugurated by the article ‘Incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics’ by D. J. Bottomley et al. [Surf. Sci. 603 (2009) 97

Response to the Reply by D. J. Bottomley et al. to the comments written by J. C. Eriksson and A. I. Rusanov entitled Additional remarks related with the discussion inaugurated by the article Incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics by D. J. Bottomley et al. [Surf. Sci. 603 (2009) 97

Response to the Reply by D. J. Bottomley et al. to the comments written by J. C. Eriksson and A. I. Rusanov entitled Additional remarks related with the discussion inaugurated by the article Incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics by D. J. Bottomley et al. [Surf. Sci. 603 (2009) 97]

Current state and problems in surface tension of solids, logical and experimental analysis of basic equations

Of the four basic thermodynamic equations for the surface tension of solids: the generalized and classical Lippmann equations, and the Shuttleworth and Gokhshtein equations, only the Gokhshtein equation has been confirmed experimentally. The generalized Lippmann equation is generally considered to be more universal, since three other equations could be derived from it. This fact has been widely accepted, but recently it was reevaluated in two opposite ways. In the first approach, the experimental verification of the Gokhshtein equation should support the correctness of the generalized Lippmann and Shuttleworth equations. In the second approach, the incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics raises doubts upon all its corollaries, including the generalized Lippmann and Gokhshtein equations. Both these logical approaches are shown to be erroneous, since the Gokhshtein equation cannot be correctly derived from any of the above-mentioned equations, and the opposite is also true: neither the generalized Lippmann nor Shuttleworth equations could be derived from the Gokhshtein equation. The high sensitivity of the contact electric resistance method to negative adsorbate charge allows detail investigation of the kinetics of the charge transfer during anion adsorption. For the fist time, this permits a tentative approach to quantify the potential dependence of the partial charge transfer during halide ions adsorption on IB metals.

Additional remarks related with the discussion inaugurated by the article “Incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics” by D. J. Bottomley et al. [Surf. Sci. 603 (2009) 97

Jan Christer Eriksson and Anatoly I. Rusanov critically analyze a paper titled 'Incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics' by D. J. Bottomley and co-researchers. According to him, the problem of double counting that Bottomley and co-researchers supposed to be due to involving pairs of terms of the kind xdy + ydx, is not a true research issue but rather a pedagogical one. Within the formal scheme adopted by Gibbs, this problem is properly dealt with by means of a Gibbs Duhem condition. The critics underline that the incompatibility with the mathematical structure of thermodynamics erroneously claimed by Bottomley and co-researchers would apply not just to solid but to liquid interfaces as well, thus invalidating even the firmly rooted Gibbs surface tension equation.

Reply to: “Comment by P. Hecquet on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Reply to: “Comment by P. Hecquet on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Comments on the article entitled “Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” by D.J. Bottomley, Lasse Makkonen and Kari Kolari [Surf. Sci. 603 (2009) 97

In the Shuttleworth’s equation g ij = γ δ ij + d γ / d ε ij , γ is the surface energy and g ij is the surface stress with respect to the corresponding bulk quantity. At equilibrium and T = 0 K, the bulk energy is the cohesive energy and the bulk stress is zero ( p = 0 ). For i = j ( ε ii is hydrostatic) and for a flat surface, we show that the equilibrium surface stress g ii corresponds to a surface pressure located mainly at the first monolayer and that the presence of the surface energy γ in the Shuttleworth’s equation results from the matter conservation rule. Indeed, γ is an energy calculated per constant unit area while the atomic surface varies with the deformation as ( 1 + ε ii ). The equilibrium surface stress g ii present at the surface is parallel to the surface. When g ii is positive, this signifies that the surface atoms tend to contract together in the direction i even if the bulk pressure p is zero.

Hierarchy of equations for the surface tension of solids

Of the four main equations in thermodynamics for the surface tension of condensed matter, i.e. the generalized and classical Lippmann equations and the Shuttleworth and Gokhshtein equations, only the classical Lippmann and Gokhshtein equations have been confirmed experimentally. The generalized Lippmann (Couchman–Davidson) equation is considered to be more universal, since three other equations could be derived from it. Although this fact has been widely accepted, it was recently reevaluated in two opposite ways. In the first approach, the experimental verification of the Gokhshtein equation should support the correctness of the generalized Lippmann and Shuttleworth equations. In the second approach, the incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics throws doubts upon all its corollaries, including the generalized Lippmann and Gokhshtein equations. However, both of these approaches are here shown to be erroneous, since the Gokhshtein equation cannot be correctly derived from any of the above-mentioned equations, and the opposite is also true: neither the generalized Lippmann nor Shuttleworth equations could be derived from the Gokhshtein equation.

Might Dark Matter and Energy be Intrinsic Properties of Space?

It is shown that if a volume element V, of space is assumed to have intrinsic energy E, then basic principles of mechanics, thermodynamics and special relativity lead to the equation of state: E=pV, where p is the pressure. When this equation of state is incorporated in the Einstein equations it leads to the prediction that the orbital speed of matter circling a visible galaxy embedded in a spherical galactic halo should be relativistic, in disagreement with observations. However, it also leads directly to the interesting notion that the inertial mass of such a medium can be understood as a resistance to being compressed via Lorentz contraction. It is then shown that the mathematical structure of thermodynamics suggests another plausible definition of pressure if we allow for the possibility that the intrinsic energy of spacetime may not be described by the same work-energy relationship as ordinary matter. This additional possibility leads to the equation of state: E=−pV. While both of these equations of state describe forms of energy that are quite unlike ordinary energy, neither alone is able to account for observed rotational velocity curves of matter orbiting visible galaxies. Therefore, the possibility that space has two distinct components of energy is investigated. This results in a plausible, two-component equation of state in which the former equation of state is tentatively identified as the “dark matter” (DM) component, the latter as the “dark energy” (DE) component. The effective equation of state of space, accounting for the presence of both components, may then be written in the form: p=w e, where e is the total energy density, p the total pressure, and w represents the fractional excess of DM over DE (and therefore satisfies: −1≤w≤+1). Given the wide range of possible spacetime properties implied by this equation it appears to be a viable candidate for explaining observations presently attributed to the presence of both DM and DE. Specifically, the static, spherically symmetric solution of Einstein’s field equations, neglecting effects of ordinary matter, predicts the inverse r 2 distribution of intrinsic space energy required to explain observed constant rotational velocity curves for matter in circular orbits around visible galaxies embedded within spherically symmetric galactic halos. The proposed equation of state is also capable of describing regions of space undergoing accelerated expansion as regions where DE is dominant (i.e., w<−1/3).

Reply to: “Comment by H. Ibach on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Reply to: “Comment by H. Ibach on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Reply to: “Comment by V.A. Marichev on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Reply to: “Comment by V.A. Marichev on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Reply to: “Comment by J.E. Eriksson and A.I. Rusanov on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Reply to: “Comment by J.E. Eriksson and A.I. Rusanov on: Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” [Surf. Sci. 603 (2009) 97

Comments on the article entitled “Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” by D.J. Bottomley et al.

Jan Christer Eriksson and Anatoly I. Rusanov present their views on the article entitled 'incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics'. They derive the the general free energy differential expression for a solid fluid interface to continue their discussions. They also focus on discussing the derivation of the Shuttleworth equation within a thermodynamic framework. A pure solid phase composed of a single component is considered for simplicity that is surrounded by a adsorbing and inert gas at low pressure. They also assume that the symmetry of the solid surface is sufficiently high so as to make the surface two-dimensionally isotropic. They have been able to obtain the relevant Helmholtz energy differential expression for an arbitrarily positioned dividing surface by assuming the excess number of moles of the solid component to always remain the same on the basis of the first equation.

Comment on “Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” by D.J. Bottomley, L. Makkonen, K. Kolari [Surf. Sci. 603 (2009) 97

Comment on “Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” by D.J. Bottomley, L. Makkonen, K. Kolari [Surf. Sci. 603 (2009) 97

Comments on the article entitled “Incompatibility of the Shuttleworth equation with Herman’s mathematical structure of thermodynamics” by D.J. Bottomley, Lasse Makkonen and Kari Kolari [Surface Science 603 (2009) 97

Comments on the article entitled “Incompatibility of the Shuttleworth equation with Herman’s mathematical structure of thermodynamics” by D.J. Bottomley, Lasse Makkonen and Kari Kolari [Surface Science 603 (2009) 97

Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics

We show that three independent derivations of the Shuttleworth equation, arguably the second most important equation in surface physics, are inconsistent with Hermann’s mathematical structure of thermodynamics [R. Hermann, Geometry, Physics and Systems, Marcel Dekker Inc., New York, USA, 1973 (Chapter 6)]. The possible implications of this result are discussed.

On the Mathematical Structure of Thermodynamics with Internal Variables

The mathematical properties of thermodynamics with internal variables are investigated in a general framework, both for the local and gradient theory. The consequences of the Second Law of Thermodynamics on the constitutive equations, together with some peculiar properties of the equilibrium states, are proved. The evolution equations of the internal variables are derived as a system of Hamilton equations resulting from a suitable Legendre's transformation.

GENERALIZED SYMMETRIC NONEXTENSIVE THERMOSTATISTICS AND q-MODIFIED STRUCTURES

We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q↔ q-1 symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of nonsymmetric. Tsallis statistics. Basic propreties and analogies with quantum groups are discussed.