|In 1975, American sociologists James Dabbs and Neil Stokes found that beautiful people are given more volume of personal space when moving in public, a proof that thermodynamics applies to humans socially. In 2002, American electrochemical engineer Libb Thims found prove of Beckhap's law, that beauty is inversely proportional to brains, on average.|
Descartes | Spinoza
The following is a noted maxim of Rene Descartes:
Dutch philosopher Benedict Spinoza, from an early an age, was said to have been said to have been strongly impressed by this Cartesian ideology.
In hmolscience, often when physics, chemistry, and thermodynamics terminologies are seen being employed to explain social phenomena and social questions, the objection arises to the effect of: “where is the proof?” or “has this been tested by falsifiability”, of the Karl Popper test of science variety, “can the theory make predictions” that can be tested, and so on. The following 1945 statement by American historian Morris Zucker in objection to physicists employing physics theory, such as relativity, to explain sociology and history, seems to hit the nail on the head: 
“We will soon have the occasion to discuss the social philosophies of some really great physicists when they deign to pass judgment on social questions. Here we are concerned with an attempt to engraft ‘relativist’ history through the medium of relativist phraseology. The frame of reference, lines of force in a gravitational field, the time-space continuum, all these are noble conceptions in physics where they are endowed with precise meaning and have been subjected to experimental proof. Writers have attempted to smuggle these conceptions into history by the simple expedient of employing the same idioms. They sound the same, but have not the same meaning. Let them use facts instead of phrases, proof instead of analogies.”
In 2010, another example comes from Iranian-born American chemical engineer Ali Mansoori who, at the end of a guest lecture on human thermodynamics given by American electrochemical engineer Libb Thims, given to bioengineering thermodynamics students, at the University of Illinois Chicago, Mansoor, the professor of the class, asked Thims, in followup Q&A, “has this been proved anywhere?”
Swiss mathematical physicist Leonard Euler, with his circa 1740 “reciprocity relation” is the so-called mathematical proof behind the condition for an exact differential, and hence the mathematical proof behind the existence of state functions, in particular entropy, of thermodynamics.
In circa 1860, German physicist Rudolf Clausius gave his famous “proof of the impossibility of perpetual motion of the second kind”, according to which perpetual motion violates the second law of thermodynamics.
In 1882, German physicist Hermann Helmholtz, in his “On the Thermodynamics of Chemical Processes”, famously proved that free energy, not heat, is the true measure of chemical affinity. Belgian chemist Theophile de Donder, supposedly, also gave a similar proof in 1922, but by that time, Helmholtz's proof had already been absorbed into the 1923 textbook of Gilbert Lewis, and hence modern chemical thermodynamics, as it is currently known.
The subject of "thermodynamic proofs" are a bit of a complex subject. They are, in a sense, mathematical proofs—sets of arguments used to deduce a mathematical theorem from a set of axioms—combined with proofs and measurements found from physical experiments on nature in respect to heat, work, and energy. The examples of Q&A’s behind attempts to prove something as simple as, for example, Boyle’s law, something first arrived at via experimental data obtained from the pneumatical engine, give examples of the issues at hand. 
See main: Dabbs-Stokes studyThe 1975, American sociologists James Dabbs and Neil Stokes, in their article "Beauty is Power: the Use of Personal Space on the Sidewalk", presenting the results of a study in which the time lapse filming of pedestrians observed from above walking along a sidewalk, which found a number of quantitative findings, one being that a beauty causes a volume expansion, meaning that a beautiful person is given or allotted more personal space when moving through crowds, a finding measured in inches increase in volume.  This would seem to be one of the first proofs of a connection between beauty, mechanisms of human chemical reactions, and pressure volume work, as quantified in human chemical thermodynamics.
Beckhap's law proof
See main: Beckhap’s law proofIn 2002, American electrochemical engineer Libb Thims, using college graduation photo attractiveness ranking data and intellectual difficulty of college degree obtained data proved of Beckhap’s law, that beauty and brains, on average, are inversely proportional.
Specifically, to determine if physical attractiveness, statistically, is inversely proportional to intelligence, on average, Thims had one group of people rate the physical attractiveness of 2,018 college graduation photos, graduating classes of 1969 and 1972 at the University of Illinois at Chicago, and had a second group of people rate the intellectual difficulty of each degree obtained, for the people in those photos, albeit only being shown the name of the degree.
These two data sets were sorted by sex and grouped into similar categories. The results confirmed the theory. In the graduating classes of 1969 and 1972, for example, 670 female students obtained 67 different degrees. By comparing females who obtained science-related degrees, among other related groups, we obtain the plot shown below: 
Description: A plot of the ranked data results, of the group "female science majors", from the 2002 study of 2,018 University of Illinois at Chicago (UIC) college graduation photos, graduating classes of 1969 and 1972, showing that attractiveness is inversely proportion, on average, to intelligence, a finding which corroborates Beckhap's law.
Key: P = psychology, B = biology, C = chemistry, and M = mathematics, each with 41, 20, 13, and 21 students, respectively. Similarly, A = physical attractiveness (of group); on a scale of 7.0 = most physically attractive to 1.0 = least physically attractive; and I = intellectual difficulty (of degree); on a scale of 100 = most intellectually difficult to 10 = least intellectually difficult.
A similar inverse trend was found with male engineering students, namely that the physical attractiveness of students, on average, was found to be inversely proportional to intellectual difficulty of degree obtained.
Thims then attempted to explain this finding by correlating the initial state Gi and final state Gf of the free energy change for a typical mating reaction to bulk values of attractiveness and intelligence involved in mate selection. A solution was found using the following two assumptions, first that enthalpy is proportional to physical attractiveness:
This would concur, in some sense, with Frederick Rossini's 1971 "Chemical Thermodynamics in the Real World" argument that enthalpy is a measure of "security" in social reaction existence, meaning that people will tend to want to bond with physically attractive individuals in relationships, and hence be seemingly more "secure" in their social existence or in the social structure, whereas less physically attractive individuals will tend to remain single, e.g. homebodies, cat ladies, and or outcasts, e.g. hobos, bag ladies, etc., give or take, baring more detailed discussion.
The second assumption made was that entropy is inversely proportional to intelligence:
This would concur, in some sense, with Stephen Hawking's 1996 argument that reading decreases the neurological entropy of a person by so many units, meaning that intellectual mastery would be inversely proportional to entropy of a person, in a roundabout sense, using a combination of the 1862 entropy as a measure of disgregation model of Rudolf Clausius and the 1882 characterization by Hermann Helmholtz of the magnitude of entropy |S| as the measure of disorder of the particles of the system with respect to each other.
With these approximations in place, one can employ intelligence and physical beauty as correlative measure of entropy and enthalpy, respectively, which can thus be used to represent the instantaneous 'state' of the reactive system at any given second on going from reactants to products. These, in turn, can then be substituted into the Gibbs equation:
to yield for an inverse relationship plot. Skipping over much of the derivation and discussion, using the two above approximations, and assuming that initial state of the reaction, in which two individuals, one male molecule Mx and one female molecule Fy, of varying levels of intelligence and beauty, is the day the pair fall in love at first sight, that they pair conceives one child, Bc, three years later, and that the end state of the reaction, coincides with the point of the fifteenth year of the growth of the child, after which the precipitate child molecule begins to detach from the parental structure. This gives the following simplified overall reaction mechanism:
On this model, the following variables can be be defined at day one (-3 years before conception) and the final day (+15 after conception):
Gibbs free energy of the state of the child, Bc, detached at age 15. Gibbs free energy of the state of two reactants, the male Mx and female molecule Fy, at the point of love at first sight. Enthalpy of the state of the child, Bc, detached at age 15. Enthalpy of the state of the two reactants, the male Mx and female molecule Fy, at the point of love at first sight. Entropy of the state of the child, Bc, detached at age 15. Entropy of of the state of the two reactants, the male Mx and female molecule Fy, at the point of love at first sight.
Using these time-specific variables, through a bit of substitution, one can derive the following result: 
which says that, owing to the constraints of the Gibbs equation, otherwise known as the combined law of thermodynamics, the physical attractiveness of the individual, in this case the male, will vary inversely with the intellect of the individual, on average, at the initial start to a typical romantic male-female reaction.
There are many issues, to note, with this proof, one being that the second assumption, that of entropy, using the disorder model of entropy, in human reactions, being inversely proportional to intelligence (mental order), is derived from gas theory, particularly the Boltzmann chaos assumption, in which particles are assumed to have non-correlative velocities, which is not the case with human molecules.
In 1992, French-born English ecologist-philosopher Edward Goldsmith, in his The Way: An Ecological World-View, attempted to argue, on the logic of the views of Belgian chemist Ilya Prigogine, that the laws of classical thermodynamics cannot be applied to living things, and included an appendix section devoted to a supposed ten-page proof that “the entropy law does not apply to behavior within the ecosphere.” 
In 1869, German physicist-physiologist Adolf Fick, supposedly, attempted to give some type of ‘entropy proof of God’s existence’; the first of many so called second law based or disorder-order based proofs of God reoccurring seen ever sense.
The following are related quotes:
“The concept of psychic energy is as much justified in science as that of physical energy, and psychic energy has just as many quantitative measurements and different forms as has physical energy. The burden of proof falls on those who deny psychic energy, not on those who acknowledge it.”— Nicolas von Grot (1898), “The Terms of the Soul and Psychic Energy n Psychology”
“What does economic power mean in a system theoretical rather than in a political sense? We don’t know? Consequently, we cannot define a set of adjugate variables that describe the behavior of a macroeconomy. However, I would like to go one step further. While I cannot prove this to be correct, I am personally convinced that any real system that can meaningfully be describe by a differential equation model—and macroeconomic systems are among those without any question—possesses some sort of ‘energy’ that obeys the law of conservation of energy. It is just that, to my knowledge, nobody has ever looked into systems, such as macroeconomies, from quite that [thermodynamic] perspective and tried to formulate a meaningful and consistent definition of the terms ‘energy’ and ‘power’, and from there derived a set of adjugate variables, the product of which is ‘power’. This would be a very worthwhile topic for a PhD dissertation.”— Francois Cellier (1991), “Modelling in Nonequilibrium Thermodynamics”
1. Merriam-Webster Collegiate Dictionary, 2000.
2. Zucker, Morris. (1945). The Philosophy of American History: The Historical Field Theory (pgs. 165-66). Arnold-Howard Publishing Co.
3. (a) Thims, Libb. (2002). “UIC: Attractiveness vs. Intelligence Date: 2,000 graduation photos rated for attractiveness and undergraduate degrees per each photo rated for intellectual difficulty”, IoHT Research Project.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two) (UIC: Attractiveness vs. Intelligence Study, pgs. 671-72). Morrisville, NC: LuLu.
4. Dabbs, James M. and Stokes, Neil A. (1975). “Beauty is Power: the Use of Space on the Sidewalk” (abs), Sociometry, 38: 551-57.5. Goldsmith, Edward. (1992). The Way: An Ecological World-View, (pgs. 13-14) (Appendix One: Does the Entropy Law Apply to the Real World?, pgs 439-48). University of Georgia Press.
5. Goldsmith, Edward. (1992). The Way: An Ecological World-View, (pgs. 13-14) (Appendix One: Does the Entropy Law Apply to the Real World?, pgs 439-48). University of Georgia Press.
6. Thermodynamic Proof – PhysicsForum.com.
● Thims, Libb. (2011). “Thermodynamic Proof that Good Always Triumphs over Evil”, Journal of Human Thermodynamics, 7: 1-4.
● Scientific evidence – Wikipedia.