● This JHT beta articles has passed through the beta review process and is now a published article in the Journal of Human Thermodynanics, the beta-stage peer review version and discussion of which (shown below) is archived here.

Article
A Thermodynamic Methodology for Evaluating of Friendship Relations Stability
(a JHT submission)

Tiny url
http://tiny.cc/3ulli (short copy-n-paste utility link to this page)

Authors
Mohsen Mohsen-Nia
Contact: moh.moh@cheme.caltech.edu
Thermodynamic Research Laboratory, University of Kashan, Kashan, Iran
Division of Chemistry and Chemical Engineering, Caltech, Pasadena, California, USA
F. Arfaei
Department of Human Science, University of Kashan, Kashan, Iran
H. Amiri
Thermodynamic Research Laboratory, University of Kashan, Kashan, Iran
A. Mohsen Nia
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

Received: 21 Oct 2011 (original); Reviewed Oct 22 - (add); Published (view): 07 Dec 2011

Reviewers

● Libb Thims
About: JHT founding editor

Threads: Erich Muller credit (Oct 22), Pan et al 2005 (Oct 25), Entropy and your Dong (Oct 26), Listing reviewers in the publication (Oct 26), Kenoun's review (Oct 28), On Jurgen's review and view of temperature (Nov 15).

● Jewgeni Starikow (Hmolpedia member: Donquizote5)
About: author of Modern Methods for Theoretical Physical Chemistry of Biopolymers (2006); favorite topic: entropy-enthalpy compensation.

Comment one: “To my mind, the publication proposal you have asked about, is not to be published in Hmolpedia, for it has in fact nothing to do with thermodynamics at any rate.”
Comment two: “Well, if it's going to be published, then, sure, it's fine with me ... I have in effect no other comments ... And I'm now in fact busy with submitting my second paper on George Augustus Linhart and his bright thermodynamic ideas, as well as about how G. A. Linhart's ideas are connected with those of Gilbert Newton Lewis.”

● Sean O'Reilly (Hmolpedia member: seanor59)
About: moral philosopher, noted for 2001 sexual energy advice book How to Manage Your Dick, with its chapter on “Entropy and Your Dong”.

Review: “I found this article pretty interesting. I am not a mathematician or a molecular biologist but would suggest that you consider some of the extraneous things like religion, belief, love, etc., to be analogous to electron rich donors and what we call evil, excess or vice to be akin to electron poor elements. Clearly, what an electron rich mixture will add is considerably more valuable, in cases, where electrons are needed. Covalent bonds, etc., are more readily formed. Just a thought” (thread: things that cannot be counted) (Oct 25)

● John Bryant (Hmolpedia member: thermoeconomist)

About: author of the 2009 book Thermoeconomics.
Review: “Had quick look at the study - interpersonal relationship research is not my field, wouldn't a qualified psychologist be a better bet? In passing, I thought the connections towards the end were a bit tenuous, but I can't claim to be an expert in any sense.” (Oct 25)

● Anon Reviewer 1
About: Ecological thermodynamicist

Comments: “Understanding DMRSekhar's comments on the lack of peer review, it is still not normal to list the reviewers in the publication. The "entropy and your dong" reference for one reviewer alone is enough for most 'academics' to stop considering the publication alone. Please reconsider the reviewer referencing accordingly.

I first need to read Erich Muller's article. Are the affiliations correct? Reference checking is a terrible, but necessary task in reviewing an article. Are the references truly correct/relevant? Who should check them? More information on the study needs to be included. Especially the notions of 'emotional intelligence' 'introvert' and 'extrovert' need to be explained in greater detail as to their definition and correlation/analogy to thermodynamic variables.

Refrain as the editor of adding or changing the article itself. Suggestions of changes are acceptable, but the editor should not actually modify the submission in any way. Not familiar with the Leonard-Jones potential, so cannot comment on its applicability. With regards to the personality test, the difference and uniqueness need to be statistically quantifiable terms. The corresponding author from the Dept. of Human Science is hopefully a psychologist or someone qualified to explain those statements further.

Why was the particular personality test chosen? The statistical analysis of results should be elaborated further. The concept of 'stability' is not well defined even in mathematics, how is it defined in their study?” (Oct 25)

● Robert Kenoun (Hmolpedia member: Wrk003)
About: author of the 2006 A Proposition to Theory of History and Social Evolution (theory: social internal energy minimization).

Response: “In my view, when a complex system’s behavior is analyzed by the laws of its constituent subsystems (although to some extent they may influence it behavior but generally insufficient) to explain the behavior of the complex system, they fall short of explaining it due to the fact that the complex system have added characteristics not fully explained by the laws that govern the behavior of subsystems.

Let us look at the insufficiency of the plot presented by Lennard Jones potential model when applied to human relations.

1 - In very small distances the plot shows strong repulsive forces between humans. That may be true for two people who are fighting each other but what about two people making love to each other. In the later case the forces are attractive but the plot does not support this scenario.

2 – In very long distances the potential forces could be zero, positive or negative but the plot shows these forces are zero only.

But what about the loving relationship between mother and son that due to circumstances they are living in two different states. The potential forces between them are still attractive and strong even though they live far apart. What about the bitter husband and wife that have divorced each other and live in two different states. Despite far distances between them the forces between them are repulsive. And finally, what about one way love relationship, one partner madly in love with his girlfriend but the girlfriend not so much with her boyfriend. Such one way attraction can never be found in molecular level. In molecular level attraction or repulsion comes from both sides, no exception. The following plot illustrates the cases we discussed above:

This plot definitely represents a good percentage of people, not a minority. Now the philosophical question here is this. If we can take a law from the simplest system and apply it to a complex system and expect it to work, would that be also possible to take a law from the complex system and apply it to the simplest system and expect it to work? Does the law of reciprocity apply? If it does, then the plot shown above should also explain the behavior of systems at molecular level. Does it? Not really. So, if it doesn’t, then why should we insist that the other way around is a valid approach.

With this logic I intend to say that the behavior of a complex system cannot be defined by basic laws at the atomic and molecular level. There is much more to that. Complex systems possess a great deal of other characteristics all emerged from the chain of subsystems in their hierarchy influencing their behaviors. This is not to say that the laws of thermodynamic do not apply to living beings. Yes they do. But we have to be careful how to apply them.

So, in my view this plot that explains the repulsive and attractive forces at molecular level is insufficient and inaccurate when applied to human relations. When so many cases are not explained or supported by a theory, the theory has a weak foundation, and obviously, in this case, it is incapable of producing accurate and falsifiable predictions; a scientific process for benchmarking the strength of a theory.

The other thing that I do not see in this article is the verification of the theory based on the collected data. I do not see how this data proves the accuracy of the theory based on the plot presented. Does the measured data, when plotted, produce similar or identical plot like the one plotted by theory? If I am wrong in my assessment, it would be beneficial to correlate the experimental data and the theory to enhance the credibility of the research. Let us not forget that culture is a huge factor in this study (complex system’s characteristic not covered by the laws at molecular level) and a similar study in US will produce enormously different results.” (Oct 28)

● Jing Chen (Hmolpedia member: JingChen)
About: author of The Physical Foundations of Economics: an Analytical Thermodynamic Theory (2005).

Review: “I read the paper and agree with John Bryant’s review.” (Oct 31)

● DMR Sekhar (Hmolpedia member: DMRSekhar)
About: chemical engineer, genopsych (anti-entropy DNA psyche) theory promoter

Review: “I read this article though not a specialist in the field. The authors tried to give scientific explanation to friendship stability based on their experimental (survey) work. Anon reviewer 1, pointed out, “the notions of 'emotional intelligence' 'introvert' and 'extrovert' need to be explained in greater detail as to their definition and correlation/analogy to thermodynamic variables.” The authors should take note of it while revising the article.

I suggest that the authors should see if they find any analogy between friendship stability and the substance stability ideas of Prof G. Gladyshev and the same may be included in the discussion part.

Because this article is already here at this site (deemed published) it is under Post Publication Open Review which allows the authors to select/invite potential reviewers. Kindly ask the authors to suggest one or two senior reviewers in this field who can give a favorable recommendation. Kindly do not reject this article because this is an experimental work. Allow the authors to revise keeping the comment of Anon Reviewer 1 and my suggestions here” (thread: comment, 31 Oct).

● Jurgen Mimkes
About: head of the econophysics and sociophysics department at the University of Paderborn, Germany.

Review: “In thermodynamics of metals or salts the inter-atomic (Lennard-Jones) potential may be obtained experimentally using models like the Grueneisen–Debye model (J. Mimkes, M. Luebbers, H. H. Thomas. (1994). "Thermophysical Properties of cubic elements", Thermochimica Acta, 245:1-19). The coefficients of the attractive and repulsive potentials are given by the Grueneisen parameter G and the pressure coefficient K0.

I do not know whether or how the Eysenck Personality Questionnaire (EPQ) (Eysenck, 1975) and the emotionally intelligent test (Bar on) (Bar-On, 2000) are able to extract the parameters “r”, “s” and “e” in social systems. In heterogeneous interactions the interaction parameter (e) requires information about the “other” partner, like + or – for electrons or a specific factor for multivalent ions.

In my work on cohesion of binary societies, I have used the nearest neighbour model. For the stability of a thermodynamic or social system, one does not need to know the actual potentials. In binary (A-B) alloys and binary (A – B) societies the stability or cohesion (E) and the structure of the systems may be obtained from the difference between attraction to the “other” groups [ EA B + EB A ] and the “own” groups [ EA A + EB B]:

E = [EA B + EB A] – [EA A + EB B]

where E A B is the attraction or repulsion of A elements to the other group B, EB A is the attraction or repulsion of B elements to the other group A, EA A is the attraction of A elements to the own group A, and EB B is the attraction of B elements to the own group B. Only the sign of (E) will determine the structure of the system:

E > 0	the attraction to the other group is stronger than the attraction to the own group and leads to a sodium chloride structure AB A B A B A B, to marriage of man – woman, to cooperation of buyers – sellers etc.
E = 0	the attraction to the other group is equal to the attraction to the own group. This leads to Cu Ni alloys, to ideal integration, mixture, A B B A A A B A B B, to people shopping or children at the beach.
E < 0	the attraction to the own group is stronger than the attraction to the other group and leads to Fe Pb structure A A A A B B B B, to segregation of Sunni and Shia, Irani and Jews, Moslems and Christians.

There is one further parameter that can turn segregation into integration: temperature T. All segregated solids or liquids will be integrated as a gas. In society, this parameter T may be interpreted as tolerance, in economic systems as standard of living. At high standard of living, at high tolerance all social systems may be integrated. In heterogeneous systems with three or more different elements, the number of parameters will grow, accordingly. With four different neighbors of A: B, C, D, E we have the interaction of AA AB BA BB AC BC CC AE BE CE EE etc. In my opinion, one potential is not sufficient for heterogeneous societies.” (Nov 15)

● Josip Stepanić (Hmolpedia member: JStepani)
About: noted social thermodynamics / economic thermodynamics author; founder of 2003 journal Interdisciplinary Description of Complex Systems.

Review: “Before review, let me thank you for that opportunity to contribute with (hopefully constructive) comments to work of some of members of our community. The manuscript deals with a rather interesting, and rather novel topic. In that sense, I am glad to read such a text, and I hope that the authors will continue their work and develop further the methodology.

There are several comments I have about the manuscript:

1. Title could resemble more the introductory level of the text (include in it works like "Toward development of thermodynamics methodology ...").
2. I miss some basic fit of the Lennard-Jones potential to collected data, but ...
3. It is not clear why such a detailed form like LJ potential is taken. For the present level of development, some piece-wise constant potential (e.g. square well of finite depth) suffices,
4. Suppression of mentioning thermodynamics in sections Methodology and Results would enhance consistency of the text.

Kind regards.” (Nov 15)

● Jurgen Mimkes (reply two)

Reply (to thread: On Jurgen's review and view of temperature): “Libb, my interpretation of temperature T in social science has indeed been chosen by the phonetic word tolerance. But this is based on the second law of thermodynamics and the Lagrange principle L = U – T S → minimum! U is the energy of cohesion, which is negative in physics. T is temperature and S the entropy. We both may feel that sympathy or love as cohesive energy of societies must be expressed in a positive way:

- L = - U + T S → maximum

Renaming - L = L* and - U = E leads to the social Lagrange principle:

L* = E + T S → maximum!

Happiness L* of society is determined by the strength of emotional cohesion or love E. We also have the terms T and S. Entropy is a measure of disorder, of individual freedom (of others). Many people do not like disorder or individual freedom of others, but happiness of society will only be at maximum, if everybody tolerates (T) disorder (S) due to the freedom of others. Again the social Lagrange principle:

L* = E + T S → maximum!

Happiness L* of a society is at maximum, if the emotional cohesion E within the society and the tolerance T of individual freedom S are at maximum. Entropy S = ln P is dimensionless. The functions L*, E and T have the dimension of "emotions": happiness, love, tolerance. This proves tolerance to be the proper interpretation for T in societies. In physics, L, U, T have the dimension of energy: free energy, cohesive energy and mean energy or temperature. In economic systems L, U, T have the dimension of money: L: "free" capital (?) corresponding to free energy, U: capital, T standard of living. In general, systems L, U, T have the dimension of the constant U. L is the Lagrange function and T is always the Lagrange parameter.” (Nov 16)

Author[s] response

● Mohsen Mohsen-Nia (response one)
About: Iranian-American chemical engineer and fluid thermodynamics researcher

Response (to reviewers): “Thank you very much for entering my article into the beta review process. I read the constructive reviewer’s comments and really I think the “beta review process” is interesting. Actually I don’t know about the different steps of the process, but I will grateful if you let me to remove an important misunderstanding. After reading the reviewer’s comments from my dear colleague "Robert Kenoun", I think that it is necessary to explain something:

I really agree with this case that “the complex system have added characteristics not fully explained by the laws that govern the behavior of subsystems”. However, as you know, in proof by mathematical induction, first a "base case" is proved, and then an "induction rule" is used to
prove a series of other cases.

According to my opinion, there is big difference between the molecular interaction and human one. Thinking, feeling and making a decision is only for human. So the human interactions are more complicated than molecular interactions which may be affected only by physical distance. Although in the most cases, a human relation may be started after a visual contact but the physical distance is meaningless in human interactions. Using different example cases, the reviewer showed that the human interactions don't have any relation to physical distance. As we mentioned in our paper, although the molecular models such as L-J potential model can be used for describing human interactions and consequently human behaviors, but the intrinsicparameters of human system should be redefined. For instance, the effect of temperature (T) on the molecular interaction is not same as that on human interactions. Actually, this effect is meaningless. A molecule may be characterized by the size, shape and polarity. Are these important for human characterization?! Absolutely, no, they are not.

The classification of humans is based on the individual personality factors, e.g. the emotional intelligent, introvert and extrovert dimensions. These may be depended on the different factors such as gender, age, religion, culture, history and background relations especially in the first decade of life. So, in this work, the friendship relations and their stability are evaluated based on the personality differences. So the “r” in the new proposed potential model is the personality difference which totally is different from physical distance.I will be looking forward to receiving the comments by your reviewers in regard to our manuscript.” (Oct 31)

● Mohsen Mohsen-Nia (response two)

Response (to reviewers): “At first, I would like to thank you and the reviewers for taking the time and effort to review the manuscript. I would also like to thank the reviewers for their professional approach, detailed evaluation and the valuable comments. Due to the reviewers’ comments, I should describe something in the following:

1- To understand each complex system such as a society, we need to break it down into its component parts, understand their individual characters, and then see how they interact with one another to generate the whole.

2- A molecule can be characterized by its size, shape, polarity and energy. Each molecular character has a specific role in the molecular behavior of a system containing like or unlike molecules. So, a human can be characterized as a component part of a social system in the same manner. In our approach, an individual is characterized by its extroversion personality and emotional intelligent as the size and energy characters respectively.
Same as a molecule, human has different kind of energy, e.g. the kinetic and potential. In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems. Therefore, for the social system, the energy is the different aspects of human abilities such as: (I) the ability to recognize and express emotions and feelings; (II) the ability to manage and control emotions; (III) the ability to solve problems of a personal and interpersonal nature; (IV) the ability to generate knowledge to be self-motivated; and (V) the ability to use the obtained knowledge and skills for survival.

3- The interpersonal potential model can be considered using different intermolecular potential models such as the soft sphere model, L-J model and square well potential model which can be called as one parameter, two parameters and three parameters models respectively. In this work, we have used L-J model as a simple two parameters model for the interpersonal potential description.

4- The Eysenck Personality Questionnaire (EPQ) (Eysenck, 1975) and the emotionally intelligent test (Bar on) (Bar-On, 2000) are used respectively for determining of the extroversion character and the emotional intelligent of people (and ).

5- As I mentioned before, although, in the most cases, a human relation may be started after a visual contact but the physical distance is meaningless in human interactions. So, the authors believe that the friendship relations and their stability are related to the personality differences. In this work, the “r” is the personality difference which is obtained using the EPQ personality assessment test.

6- I completely agree with Professor Mimkes in this point that in heterogeneous interactions the interaction parameters require information about the “other” partner. The parameters of the potential model are different for the binaries (A-B) and (A-C) which can be obtained from the EPQ and (Bar on) tests. In other words, the obtained potential value of the pair (A-B) may be positive (+) while that is negative (-) for the pair (A-C) which respectively indicate the unstable and stable relations. However, this approach allows to study of the quantitative evaluation of human pair relations.” (Nov 20)

Beta article (draft)

Abstract
This paper presents a molecular potential model to describe the human interactions in interpersonal relationships. We propose that friendship relations can be accurately evaluated by an intermolecular force model via a simulation method using a set of individual personality characters such as emotion intelligent, introvert and extrovert dimensions as the necessary input data. Because the internal states of the human are not directly observable, the human behavior models requires the necessary human’s internal state information which is determined through an indirect estimation process. Because there are various roles for peoples across different relationships, the objective of this work is an effective effort to address the friendship satisfaction factors and consequently relationship stability. The proposed model is examined for a university-students union as a case study. As a result, using personality assessment tests, the proposed model can be successfully used to predict the stability of human friendships in the different multicultural social networks.

Keywords: human interactions, friendship, relationship stability, molecular potential model.

A human thermodynamics variables table (stylized on Irving Fisher's 1892 variable table), made by lead author Mohsen Mohsen-Nia, descriptive of the variables used in this article.

Introduction
In recent years, there has been an increasing attempt towards understanding how people react to situation and how to respond appropriately. The knowledge of human interactions is a key to success in different activities, e.g. business, friendship, marriage and life (Carrington et al., 2005; Pale et al., 2006). Due to the complexity of human interactions, in many cases, human behavior is typically modeled only at the level of a single person (Liao et al., 2006; Huynh et al., 2008). However, studies on the factors that keep people together are always of interest to the social scientists (Kelley, 1978; Hicks et al., 1970; Gatica-Perez, 2009). Of course, the stability prediction of human friendship relations and consequently the global social behavior are strongly related to the individual personality factors of single persons, e.g. the emotional intelligent, introvert and extrovert dimensions. These may be depended on the different factors such as gender, age, religion, culture, history and background relations especially in the first decade of life. However, the mutual effects of the local individual behavior and global social structure make the human behavior representation as a complex topic.

For simplicity, the global social structure may be considered as a collection of independent persons, dyad (a single pair), small interacting group and multiple people relationships (Pentland, 2007; Gibson, 2005). Therefore, this approach shows a quantitative way to study the role played by individual human personality and human interactions in shaping the kind of aggregate behavior observed at a population level in social structures. Therefore, as a key element in analyzing human behavior in social systems, a hypothetical molecular system containing single and aggregated (dimmer, trimmer and polymer) molecules can be considered. The molecular system containing interacting particles can be used to estimate the social system behavior via a simulation method.

From the thermodynamic viewpoint, the average number of molecular aggregates in a system containing different size of aggregated molecules is related to the size, shape and polarity of molecules as well as the molecular interactions. The average number of molecular aggregates, aggregate stability and consequently the thermodynamic state and behavior of the system can be evaluated by using the statistical thermodynamic theories (Mohsen-Nia and Modarress, 2007). The simulation method as proposed in this work creates a molecular thermodynamics-based model which considers an interaction potential to describe several features of social behavior especially friendship relations. This approach may be roughly named “human thermodynamics”. The term “human thermodynamics” has been first recorded by C.G. Darwin (Thomson, 1952), in which collections of interacting humans with different individual personality are considered as the thermodynamic system.

There are various “categorical” subfields of thermodynamics applied to the study of human existence. The history of human thermodynamics traces the timeline of the theoretical insight involved in the application development of molecular interactions and the laws of thermodynamics in the understanding of the human life process, both independent persons and interacting groups (Darwin, 1952; Thims, 2007).

The numbers of distinct divisional "branches" of human thermodynamics are introduced by interdisciplinary researchers. Johann Goethe (1799) introduced “relationship thermodynamics” to explain the relationship of physics and love in human societies (Adler, 1990; Swales, 2002). Cessations thermodynamics was initiated by Ludwig Colding (1843) to study what thermodynamics has to say about death. The use of thermodynamics to explain religious theory was initiated by James Joule (Joule, 1847) and later by Richard Owen as religious thermodynamics (Colding, 1843; Owen, 1849). Hermann Gossen used economic thermodynamics for the study of the use of thermodynamics to model economies as thermodynamic systems (Gossen, 1983). Philosophical thermodynamics was proposed by Gustave Hirn (1856) to study of the philosophical implications of thermodynamics (Hirn, 1868). The use of thermodynamics in social theory was studied by Henry Carey as sociological thermodynamics (Carey, 1958-1959). Francois Massieu introduced ethics thermodynamics for applying the use of thermodynamics in theories of ethics and the difference between right and wrong (Massieu, 1869).

The subject of how thermodynamics applied to the understanding of human states of happiness was studied by August Krönig as happiness thermodynamics (Krönig, 1856). Sigmund Freud (1895) used psychological thermodynamics to study of the thermodynamics of the mind or mental states (Freud, 1895). Leslie White (1943) used the thermodynamics in anthropology. He focused to study of the comparison of different cultures applied to financial matters such as debts, wealth, and interest (Erickson et al. 2003). Karl-Henrik Robèrt introduced sustainability thermodynamics to use of thermodynamics models in development of sustainability theories (Robèrt 1991). Racial thermodynamics is applied to study of the thermodynamic explanations of racism or race by Richard Delgado (Delgado, 1990). Jurgen Mimkes (1994) proposed integration and segregation thermodynamics to study of the use of phase diagrams and solution thermodynamics logic in the explanation of the integrations and segregations behaviors of mixed cultures or people (Mimkes, 1995). The framework of human statistical thermodynamics and human chemical thermodynamics were applied in generalized outline to the study of human existence from the perspective of thermodynamics by Libb Thims (Thims, 2008).

A connected field is that of human physics, which defines people as particles and crowds as fluids or flows of particles, and studies phenomenon such as crowd behavior, inclusive of abnormal states such as emergency panic behaviors, e.g. fire evacuation movements, such as discussed in the work of Xiaoshan Pan (Pan et al., 2005)

In later centuries quantitative scientific methods have grown to study of human behavior, social interactions and important motivational role of commitment and reciprocity of exchanges on social relationships stability by reducing the problem to its simplest components. Considering the relationship stability as a topic of major interest in the study of interpersonal relationships and social satisfactions, the proposed model indicates to evaluate the friendship stability by using single person’s personality factors as the input data.

Venezuelan-born English chemical engineering thermodynamicist Erich Muller’s 1998 Lennard-Jones stylized interhuman potential attraction repulsion model, with positive values for force being indicative of repulsion and negative values of attraction. [1]

In regard to the present study, the first to introduce the concept of an “interhuman potential”, modeling pairs of humans interacting socially “similar to that of insignificant molecules” was Venezuelan-born English chemical engineering thermodynamicist Erich Muller who in his 1998 article “Human Societies: A Curious Application of Thermodynamics” employed the Lennard-Jones potential model, a mathematically simple model first proposed in 1924 by English mathematical physicist John Lennard-Jones that approximates the interaction between a pair of neutral atoms or molecules, to explain social attractive and repulsive forces thermodynamically. [2]

Muller illustrates his interhuman potential diagram pictorially, as shown adjacent, which he captions as follows:

“The solid line shows in a qualitative way the intermolecular force for two simple molecules as a function of the distance of their centers. A positive value indicates repulsion among molecules, and a negative value, attraction. The relation to human interactions is evident. An isolated individual (the sunbather) is at peace without interactions from other humans. Nevertheless, he may come relatively close to other individuals for certain occasions (like going to movies). Too close an encounter [as occurs during a fight], however, usually leads to repulsion.”

This paper, similar to Muller's original model, presents the results of a questionnaire and interview style study of 69 college subjects, the data of which is interpreted in terms of a Lennard-Jones potential attraction repulsion model.

Theoretical framework
The theoretical structure of this study is based on the molecular interactions in a thermodynamic system and their influences on the phase stability and phase transitions of different fluid mixtures e.g. binary mixtures containing different types of molecules. In other words, we assume that molecules experience intermolecular repulsive and attractive forces as well as external forces e.g., resulting from electric and magnetic fields. So, accounting for molecular interactions, ultimately creates an opportunity for predictions of the thermodynamic phase behavior. Typical evaluations require an accurate model for the intermolecular potential for describing the interaction between two particles in a specific field force. The intermolecular potential depends not only on their separation distance but also on their temporary and permanent characteristics.

The resulting particle trajectory in such systems can be completely used for describing the human relations and friendship stability prediction. Factors such as love, commitment, relationship satisfaction, religion and social culture can be consider as the external forces that affect the human interactions. So, the quantitative analyzing of the interpersonal relationship may be achieved by introducing an effective interpersonal potential model.

Factors that influence relationship stability have been studied by various researchers. Factors such as love (Gruenbaum, 1976), marital satisfaction (Lenthall, 1977; Levinger, 1966), and life-cycle stage (Rolllns and Feldman, 1970) have been found to be associated with stability of relationships. Much of the research on relationship stability has actually focused on marital stability, thus there are limiting knowledge of the factors that are associated with stable relationships. Therefore, in this work, the effects of these factors are globally considered for determining the interpersonal potential model and its parameters.

Methodology
The subjects participating in this study were volunteer undergraduate students of chemistry department at the Shiraz University (Iran) in December, 2010. They were together at least for three years. The sixty nine subjects completed the first questionnaire and interview schedule. Nine of these subjects did not complete the second questionnaire and interview. The subjects ranged in age from 21 to 26, with a mean age of 22.8. There were 22 (37%) male subjects and 38 (63%) female subjects.

The friendship and reciprocity of exchange with each friend were measured in a team work project in the physical chemistry laboratory by using an interview schedule and visual inspection. The interview was conducted by a same-sex interviewer, and the subject was asked questions about his or her happiness in the friendship and reciprocity of exchange in order to examine the level of friendship stability. Subjects also indicated the degree of personal commitment to each relationship, stability of each friendship was assessed by determining whether the friendship maintained for the project’s work collaboration.

Subjects also completed two questionnaires as the personality and emotional intelligent tests. In this research work, The Eysenck Personality Questionnaire (EPQ) (Eysenck, 1975) and emotionally intelligent test (Bar on) (Bar-On, 2000) which were normalized for Iranian society were used as the personal and emotional intelligent tests respectively.

The results of the personality and emotional intelligent tests are used for determining the parameters of the proposed interpersonal potential model. Thus the quality and stability of friendship can be evaluated by the interpersonal potential model by using the individual personality and emotional intelligent data.

To avoid unwarranted complications, it proves useful to restrict our choice to those models established for no more than two independent parameters (e.g., Lennard Jones molecular potential model). The Lennard–Jones (L-J) potential for a pseudo-pure system is defined by:

Figure 1: the schematic diagram of the interpersonal L-J potential model.

where for a molecular system, ε is the depth of the potential well, σ is the finite distance at which the inter-particle potential is zero and r is the distance between the particles. [2] The schematic diagram of L-J model is shown in Figure 1 (adjacent). As an interpersonal potential model, ε indicates the energy at the bottom of the potential well that accounts for human attraction, while σ provides a barrier for human repulsion. The parameter values can be established for any person by applying the EPQ and Bar-on test results.

In a personality test, we are talking about what makes that person different from other people, perhaps even unique. This aspect of personality is called individual differences. Instance, some people are neurotic, others are not; some people are more introverted, others more extroverted; and so on. The difference of EPQ test score is considered as r in the potential model. The difference of extroversion personality characteristics from the EPQ and the arithmetic average of emotion intelligent from Bar-on test are respectively considered as the barrier human repulsion (σ) and the energy parameter (ε) as presented in the potential model. In this manner, the interpersonal potential can be detected for evaluating the friendship quality as a measure of the value and importance of human friendship with a particular person in a specific society. So, it means that the stability of friendship can be predicted by interpretation of the proposed interpersonal potential model.

Results
Preliminary analyses were performed to obtain descriptive data on the subjects participated in this study. Ninety five percent of the friendships for both male and female subjects were same-sex friendships. According to our results, 79% of the friendships were stable. This difference was not attributed to the subjects. Male friendships did not differ significantly on stability from female friendships. According to our results from this study, the friendship stability did not show a meaningful difference for either males or females relations. The detailed results are presented in Table 1 (below). Totally, our results indicate that the method is able to achieve 90% accuracy at predicting friendship stability of subjects reviewed in this study.

Table 1: the obtained results of the friendship stability for different type of relations.

Although, the friendship stability has a significant impact on social satisfaction, considering the complexity, there is no a reliable practical model for the friendship behavior evaluation. Nevertheless, this work proposes a molecular thermodynamics based model to describe the friendship stability. This study indicates that although the commitment, social culture, religion and economic situation are important factors in friendship stability study but they can globally evaluated in term of the potential representing the human interactions. As a result, this study recommends that friendship relations should be truly identified by the interpersonal potential model for evaluating the friendship satisfaction and estimating the friendship stability.

References
Numbered
1. (a) Müller, Erich. A. (1998). “Human Societies: a Curious Application of Thermodynamics" (scan) (abstract) Chemical Engineering Education, Vol. 1, No. 3, Summer.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview), (Section: "Müller dispersion forces", pgs. 629-638). Morrisville, NC: LuLu.
2. (a) Lennard-Jones potential – Wikipedia.
(b) Potential well – Wikipedia.

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