Entropy

Can physics describe economy? What are the physical driving force behind the evolution and our sociological and economic activity?
In this collection of papers I argue that entropy, under a certain condition, is information; and therefore information has a tendency to increase. Based on this, the statistical properties of information networks are calculated, and in contradistinction to the classic sparse system that yields the canonical bell-like distribution, information networks are found to have a universal long tail distribution. This distribution predicts, with great accuracy, the wealth distribution; the relative poverty; and wealth inequality in the economy and the popularity of sites on the internet. This long tail distribution, which is called Planck-Benford distribution, yields correctly Zipf law, Pareto law, and Benford law.

Since Planck- Benford distribution has no free parameter it is a universal distribution and it can be applied to the analysis of polls, bestseller lists, earthquakes, etc.
When the statistics of the information network in equilibrium is applied to the economy, the universality of the distribution means that the wealth distribution in equilibrium is independent of the wealth of the country. In addition, one can show that people tend to migrate from poor countries to rich countries, and money tends to flow from rich countries to poor countries. Therefore, one might conclude that the tools of mechanical statistics can treat sociological and economic system in similar ways that are done in physics.

In this collection of papers, it shown that the “order” which is generated around us by evolution and the results of our doing can be explained by the propensity of entropy to increase; namely, by the second law of thermodynamics. Entropy is conceived by many as a disorder, however, that is true only for spares systems. In a dense system, entropy is information that is characterized by a long tail distribution. In order to apply the second law to sociology and economy, we have to define a sociological net. With analogy to the internet, in which, in principle, every site can receive and broadcast information to any other site we can describe economic network as a group of bank accounts that each one of them can receive or pay money to any other account. The distribution of links between the sites is similar to that of money in the bank accounts. This long tail distribution, which is obtained by maximizing the entropy of the net, is called Planck-Benford distribution. It is also shown that Planck-Benford distribution can predict polls distribution; Gini inequality Index in the OECD countries; the percentage of the relative poverty; the salaries of the CEO’s relative to the average salaries and the number of employees. Moreover, the Planck-Benford income distribution, being an equilibrium distribution (Max Entropy), can provide a standard tool for estimating the stability of the economy of a given country namely closer the income distribution of a country to Planck Benford distribution closer the economy to equilibrium.

Contents

Introduction

  1. Entropy Principle in Direct Derivation of Benford’s Law
  2. The Second Law and Informatics
  3. Informatics Carnot Machine in an Optical Fiber
  4. The Second Law as a Cause of the Evolution
  5. Information Theoretic Approach to Social Networks
  6. Information Theory and Thermodynamics
  7. Economic Inequality as a Statistical Outcome
  8. A Comment on Nonextensive Statistical Mechanics
  9. Sociological Inequality and the Second Law
  10. The Distributions in Nature and Entropy Principle

Conclusion

İncelemeler

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