Social Entropy          

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Alfredo Palomino Infante

Prof. Facultad de Química e Ingeniería Química, UNMSM


James H.L.Lawler

Honorary Professor of San Marcos University, Lima Perú

President of Nexial Institute, Dallas, USA







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.





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





1.         Introduction


We present a rather unusual application of the Second Law of Thermodynamics,  in order to help us to understand the increase of entropy in a human society. To do this a Boltzman type equation is used after simplifying it using the Stirling formula. Here, the state of a human society as a system  is described by the degree of dissatisfaction or satisfaction with the social, political and economic rules of a country. The human social behavior may be measured and expressed quantitatively by using a reliable poll. The results obtained with such relationship shows that the Second Law of Thermodynamics may be successfully applied to understand the human social behavior.


2.         Classical Thermodynamics   


Let us  recall some definitions of classical thermodynamics:


The mathematical treatment of the relation of the heat to mechanical and other forms of energy. Its chief applications are to heat engines and chemical reactions”.(1)


“...a physical discipline examining inter - conversions between different kinds of  energy and the exchange of energy between systems, specially in the form of heat”.(2)


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.


Entropy, S: It is defined for thermal reversible processes by the equation DS=DQ/T . Statistically Boltzman as will be shown later also defines entropy in terms of disorder. Entropy is a state function.


Gibbs Free Energy, G: It is defined as G=H-TS. where T is the temperature of the system, and G is the total energy less that energy (TS) which is unavailable. The difference is the energy that is available and also represents a state of the system.


Chemical Potential, m: Lets write the following relationship



Through this definition it was possible to open new applications of the second law of thermodynamics to chemistry , chemical engineering, biology and other fields. It let us characterize the state of a reacting as well as phase changing systems among others.



2.2       First Law of  Thermodynamics


This law establishes that the energy in the universe remains constant. Thus energy only transformed from one type into another. If we restrict it to a closed system we may write:


                                    dU = DQ + DW                                (1)


“D “:stands for differential of functions that are not state variables, and “d” for differential of state variable. This law is a postulated and doesn’t need any further demonstration.



2.3       Second  Law of Thermodynamics


The entropy production represents the existence of irreversibility. The second law may be stated in several equivalent ways, such as that the entropy tends to increase with time in any naturally occurring process. Thus, entropy is necessarily positive or zero


For any process it is possible to write:


                                    dS ³ DQ/T                             (2)


“=” 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]

established that the entropy (S) of a system may be used to characterize the thermodynamic probability (W) of the state of such system. The relationship between these variables is expressed by the following equation.


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







  Fig. 1 Distribución aleatoria de partículas según modelo de Boltzmann

Where k is the Boltzmann constant, k=R/No, No being the Avogadro number.

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.



3.         An Unsuspected Visitor


Lets postulate the following ideal scenario for our analysis. There is an extraterrestrial observer whose spacecraft is outside of our atmosphere and by the way, he is never visible to us. However, in spite of the distance, he is still able to distinguish the movement of individual human beings. Certainly, it would not take too long for him, to realize that the movements of human beings obey chaotic rules. This ideal scenario would not matter too much to him, unless he ignores the second law of thermodynamics, but indeed he does not ignore this law. Thus, such observer would conclude quickly that human beings express many forms of unusual, seemingly irrational, behavior. For example, he will be surprised looking at riots, political meetings, religious behavior, wars, etc. As a result of these observations, he would ask himself, what in hell motivates such uncommon behavior of the human beings?.


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 .



5.      Formulating the Relationship to Calculate Social Entropy


We postulate the existence of two types of contributions to the SE. First, what we name individual contribution (DSb) and second, the group contribution (DSg). Consequently, we may write:


                                   DSs= DSb + DSg                                 (5)


where SE=DSS , DSb may be considered as a typical value, which characterizes base contribution. Strictly speaking DSb will depend on such different contributions as the geographical location, racial prejudices, religion, etc.


For practical purposes, being DSb a relative value, we may consider it as a constant for each particular human community at a particular moment of history.


Now recalling Eq.(4)


DS’ = R ln W                                                              (6)


where  DS’ = DSs-DSb; N: total number of inhabitants in a chosen system (country), n: number of people in a determined state (degree of dissatisfaction). Consequenrly, n=iN; where i represent a fraction of  N. Observe that W is the characteristic probability of the state of the system as we stated earlier, that is to say the probability of the system (people of a country) to be in a particular mode  of agreement or dissagreement with the the current policital situation.[3]


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


Fig 2. Social entropy increase with social degree of dissatisfaction


For our calculation N was assumed to be 22 million and  n ranged from 0 to 0.9.



7.         Discussion and Analysis


According to the Second Law of Thermodynamics, the entropy of a naturally occurring system always increases. If we use this statement to help to understand a human society, a question arises immediately:  Why is human society not chaotic on the whole?. The answer appears to rely on society’s own ability to create organized systems and sub systems by using intelligence. Let us take any well defined human society for our analysis. A nation or any major political unit will do. We know that there are rules that must be obeyed by all people in such a system (at least in theory). These are the political laws that they obey. In[4] this way, political, economic, cultural and social rules must (or should) be well defined and assembled in theory and practice in order to avoid / prevent totally chaotic systems. To the extent that these laws are observed and followed by the individuals within the system, the system will be orderly, “regular” and avoid chaos. Those individuals who do NOT obey the laws introduce disorder / chaos into the system. Thus the disorder is a precise measure of expressed disagreement with and dissatisfaction with the rules / laws of the society.  All these variables may configure a social response, that is to say, a degree of dissatisfaction or satisfaction with the current system. As a matter of fact, if the social rules are arbitrarily applied in favor of minorities, the social entropy will increase with time more rapidly, compared to other social systems where justice favors no one and applies to everyone, particularly to large majorities. Those who do not obey are criminals, and must be dealt with as such. This forces conformity to the laws, the rules of behavior, and applies a correction / motivation to prevent chaos.


One of the key points for a rapid increase of the social entropy is the degree of civil disobedience, expressing information about internal dissatisfaction and encouraging chaos and giving rise to the eventual “birth” of leaders in a particular scenario. Consequently, we may see that social disorder comes from social dissatisfaction, hence social entropy exists and may be calculated if we are able to deduce mathematical relationships for it.  Fortunately for us, we did not have to dig too deep in order to find it.


Relative SE is possible to be approached from a Boltzmann type relationship by using statistical data concerning the degree of social dissatisfaction with the political system of a country. The calculation shows a typical shape which becomes nearly asymptotic on the large.


It is particularly interesting to realize how dictatorial political regimes in the world collapse under the same “mechanism”; that is to say a dictatorial collapsing patron. Where the social entropy accumulates to  a such extent  that a small perturbation conducts the system to a run away situation and the dictatorship has to resign and scape.


Any political system that permanently violates the Second Law of Thermodynamics, contributes itself to increase its Social Entropy. In other words it forces itself to its end. We may bring into account quite a lot of cases as examples. Thus, lets bring the case of Sukarno´s regime in Indonesia, Marco´s regime in Philipines and Fujimori´s regime in Perú.


Apparently, there are two ways for a political system to force to an apparent social order, which is by being honest and open, giving voluntary compliance with rules, or by making use of the force, which is characteristic of dictatorial regimes; but the last one works only for a very short period of time; because DSb will start increasing leading undoubtedly to the social dissatisfaction.


Human society has coined several sayings which is a sophisticated way of stating the second law of thermodynamics: remember for example: “There is no political malady which will last 100 years, and there is nobody who will go along with it”(simply because social entropy increases). Would you please remember Montesinos and his “partner” as an pathetic example?. Or remember the disorder of Alan Garcia before that?, just to rely on the Peruvian case.


8.      Concluding Remarks


SE exists and may be approximated using a Boltzmann type equation.


SE apparently has two components, one is the base contribution and the other is the group contribution, both being important to be taken into account to fully understand a particular moment of history and social behaviour.


SE may be estimated for any social system because it measures the degree of social disagreement with the current local administration. However, according to the uncertainty principle and taking into account the “aliens point of view”, human beings are also unpredictable; hence a degree of freedom should be added to the system in study, just to increase the accuracy of the calculation. This approach has not been performed  here and will be dealt in future works.


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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