# TO AN UNUSUAL  DOMAIN

## James H.L.Lawler

Honorary Professor of San Marcos University, Lima Perú

President of Nexial Institute, Dallas, USA

SUMMARY

A pseudo state function, the  “Social Entropy” (SE) is defined in order to show the application of the second law of thermodynamics to the human social behavior. This is achieved under the assumption that such  property (SE) is equivalent to the degree of social dissatisfaction (SD), of certain social, economic, or political system.  Hence, a Boltzmann type equation is used after simplifying it with Stirling formula , to obtain a rough estimative of the amount of the relative  SE in a determined  place and moment of history .

A case study related to the Peruvian society has been used here to demonstrate our hypothesis that the social entropy tends to increase with time. Similarly the degree of disorder of a thermodynamic system increases with time. Generally speaking we observe so far that the degree of disorder is a manifestation of the social dissatisfaction within the limits of the system.

# CONTENTS

1                     Introduction

2                     Classical Thermodynamics

3                     Un Unsuspected Visitor

4                     Social Entropy as Pseudo State Function

5                     Formulating the Relationship to Calculte Social Entropy

6                     A Case Study to Calculate Social  Entropy

7                     Discussion and Analysis

8                     Concluding Remarks

9                     References

# 2.         Classical Thermodynamics

Let us  recall some definitions of classical thermodynamics:

# 2.1       Some Fundamental Concepts of Classical Thermodynamics

Closed System: In classical thermodynamics, a closed system is chosen and must clearly be defined for the purpose of the study to establish the boundary within the larger universe.

Energy, E: Energy is defined as the capacity of a body for doing work.

Heat, Q: Heat is that form of energy that flows when a hot system is put in thermal contact  with a cold system. This type of energy flow is sustained by the difference of temperature between the two systems as a driving force.

Work, W : Work is any mechanical interaction between the system and its surroundings. This  has (or could have) as an equivalent effect of the raising of a weight (force times distance moved) or more commonly this may be expressed as pressure times a change in volume PV in the system interacting with its surroundings. Heat energy and work energy are forms of energy that matter does not intrinsically possess,  but they are forms of energy that flow between a system and its surroundings.

Internal energy, U: is the amount of energy which is stored in a body and accounts for the movements of atoms which constitutes the matter, it is a state function of the system and its value depends upon the chosen standard state. It is essentially the same as E for a closed system.[1]

Enthalpy, H: Enthalpy is the sum of all energy types and is usually defined as total of internal energy and work by the following relationship: H=U+PV, where, H is enthalpy,  P is the pressure and V is volume of the system.  H is a state function.

# 2.3       Second  Law of Thermodynamics

## “=” stands for a reversible process and  “ >” for irreversible process.

ã Alfredo Palomino Infante/Prof. UNMSM

# Boltzman gives statistical interpretation of the Second Law of Thermodynamics. He[2]

## S= R ln W = kNo ln W            (3)

Fig. 1 Distribución aleatoria de partículas según modelo de Boltzmann

# 2.4       Third Law of Thermodynamics

## Planck (1900)  stated that every system whose temperature approaches zero (T       +0) has zero entropy (S=0). This means that at such low temperature movement ceases and full order is achieved in a system. Eq. (4) is a mathematical way of expressing this statement. This law  is also a  postulate, just exactly as the first and second laws are.

# Suppose now that this alien visitor gets closer to the earth (remember, he is invisible to human beings) and manages to learn the reason why the human beings behave that way. Soon he would be able to understand that such apparently unusual behavior is consistently motivated by a lack of some degree of freedom; which may be summed up as a state of satisfaction or dissatisfaction. Viewed in this way, our social system may be approached through the second law of thermodynamics.

4.         Social Entropy as a Pseudo State Function

Now, leaving the alien visitor for a while. Our analysis induces us to think that  Social Entropy  is essentially a function of social state, an expression of the degree of satisfaction or dissatisfaction of  human beings. This state has to deal with the social,  political, cultural and economic situation . Thus,  if we match appropriately the alien’s  point of view and our own experience toward the human social behavior, we find logical to think on the application of the statistical form of the second law of thermodynamics in order to calculate the social entropy .

# In order to simplify the application of (6) we use the Stirling formula and find;

# 6.      A Case Study to Evaluate Social Entropy

In order to apply the relationship given above, eq. (7), to the Peruvian case, we made use of public information relative to the degree of satisfaction or dissatisfaction. This information was relatively easy to be obtained through Internet by entering web sites of specialized poll agencies. In fact, we found even more interesting to show the increase of social entropy with increase of social dissatisfaction in a rather  broad range, instead of  restricting ourselves to a particular moment of history. Thus by straightforward calculation using (7) we managed to produce a plot of social entropy vs. degree of social dissatisfaction, see Fig.2.

Degree of dissatisfaction

# 8.      Concluding Remarks

## The existence of SE implies that  the second law of thermodynamics may be applied to any society  taking it as a system ; although , we must be careful at getting reliable poll data in rather long periods of time in order to be able to estimate an appropriate answer. In this way, if we are able to show a scientific way of measuring the social behaviour as the Social Entropy is in itself, we are eventually producing a tool for the politicians no to treak people with such mistaking information  as stating that everything is all right.

9.      References

1.      Thompson, Eduard. (1999). A Unified Introduction to Chemical Engineering Thermodynamics. Stillwater Press, Orono, Maine, USA.

2.      Klotz, R. and Rosenberg, R. Chemical Thermodynamics, Basic Theory and Methods (1994) , Fifth Edit. John Wiley and Sons Inc, USA.

3.      Palomino, Alfredo. Notas sobre Termodinámica Avanzada (2000), UPG-UNSCH, Ayacucho, Perú.

4.      Krestóvnikov, A.N. and Vigdoróvich,V.N. Termodinámica Química (1980) , Traducido del Ruso por Marco Navarrete; Edit. MIR, Moscú.

5.      Lawler,James. Notes on Advanced Topics in Thermodynamics(1989), Unpublished  book.  Dallas, Texas, USA.

6.   Kirillin, V. , Sichev, V. and Sheindlin, A. (1976) Termodinámica Técnica, Traducido

del Ruso por Antonio Molina, Edit. MIR, Moscú.

ã Alfredo Palomino Infante/Prof. UNMSM

ã Alfredo Palomino Infante/Prof. UNMSM

ã Alfredo Palomino Infante/Prof. UNMSM

ã Alfredo Palomino Infante/Prof. UNMSM

ã Alfredo Palomino Infante/Prof. UNMSM

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