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7УДК.330.101
ДИНАМИЧЕСКИЕ ПРОЦЕССЫ, ЭНТРОПИЯ И ИНФОРМАЦИЯ В ПРИРОДНЫХ И
СОЦИАЛЬНЫХ СИСТЕМАХ
Катаргин Н.В., канд. физ-мат наук, доцент Финансовый университет при Правительстве Российской Федерации, г. Москва
Аннотация. Рассмотрены закономерности движения социально-экономических и природных систем в фазовом пространстве с координатами, отражающими наблюдаемые переменные ("массу") и информацию, а также скорости их изменения. Система становится доминирующей при достижении максимума фазового объёма. Стремление власти к излишнему снижению энтропии приводит к уменьшению информации и расходу ресурсов, что снижает конкурентоспособность системы.
Ключевые слова: эконофизика, энтропия, социальные системы, экономические системы, природные системы.
DYNAMIC PROCESSES, ENTROPY AND INFORMATION IN NATURAL AND SOCIAL
SYSTEMS
Katargin N., phd, docent Financial University under the Government of Russian Federation, Russia
Abstract. The patterns of the movement of socio-economic and natural systems in the phase space with coordinates that reflect the observed variables ("weight") and information, as well as their rate of change. The system becomes dominant when reaching high phase volume. The desire of the authorities to an excessive decrease in the entropy leads to a reduction of information and consumption of resources, which reduces the competitiveness of the system.
Keywords: econophysics, entropy, social system, economic system, natural systems.
Politicians, businessmen and military men start to use in practice the revolution occurring in a science, on the scales and importance of results considerably surpassing quantum revolution in the physics of the XX century. This revolution is due to using of methods and approaches developed by mathematicians and physicists in social life and economy that allows to change simple mathematical models of economic processes to more complicated ones, allowing to understand, for example, behavior of such systems in crisis. There was a new term: econophysics. The basic approaches to modeling of social and economic systems with use of econophysics:
• modelling of social and economic objects as points (ends of vectors), moving in multidimensional space on the path which can be smooth and predicted, and can sharply change in a short time (catastrophic crash);
• consideration of social and economic objects as self-ordered complicated systems with decreasing entropy, i.e. aspiring to reduce internal chaos at the expense of increase of the entropy of environments, for example, fuel burning;
• cognitive and reflective models assuming mutual training and forecasting of object and the surrounding environment, for example, interaction of the financier and a stock exchange (the theorist and an expert of such models George Soros uses it successfully);
• synergetrics, or nonlinear dynamics: mathematical methods, allowing to describe behavior of social, economic and other objects by means of systems of the nonlinear differential equations.
Essential difference of econophysics and physics is due to the investigation of objects in information space. The
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postindustrial society is characterized by that 80% working don't make material assets by hands, but create and process information. Base part of cost of production is made as results work of information processing: design, finances, trade, advertising, communication facilities, mass information, entertainments. So, struggle between states, and also criminality is moving from material space to information one. It is considered that the states of the lowest category sell raw materials and develop a heavy industry and harmful manufactures; the states of higher category develop the high technology industry, and the states of highest category (more exact: their elite) create symbols, images, financial and economic models influencing other peoples and allowing to plunder them with impunity. Example: Maintenance at high level of cost of US dollar, despite of huge debts and injection of trillions dollars to the financial system of the USA. It may be modeled as a flight of a steel list in a turbulent flow. So, USA needs in economic and social turbulence.
Basic problem of the description of social systems is an absence of the objective numerical parameters, impossibility of an exact estimation of the amount of the information containing in live structure or created by people. Money serves for a long time as a rough estimate of stability and order of a social system (from individual products of work up to states), that is its material weight and information. A basis of monetary system is gold and rare crystals, that are structured objects with very low entropy, formed by geological processes with dissipation of a big amount of energy. Amounts of natural power disappeared during formation of nuggets of gold have been
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used as a reference for a definition of expenses of energy, resources and labor for creation of ordered structures as in three-dimensional observable space (machineries, buildings), as in information field: science, education, art, social order.
Speed of accumulation and processing of information possible to consider as criterion of the stability of a system at external influences and internal indignations, so big, rich and powerful structure may be destroyed due to untimely or inadequate ones reaction.
There are physics laws of distribution of particles on energies at which the system is steady, for example, Macswell distribution for molecules of gas, Fermi distribution for electrons are known. The deviation from these distributions, for example in laser is unstable and also can lead to fast loss of energy. Money is a criterion of "power" of people and states and it is known that essential deviations from equilibrium distributions leads to wars and social cataclysms.
Estimation of "power" and stability of social structure (state, enterprise, militaries and their components) possible by using of the big set of indicators (coordinates of the end of a vector) in information-and-geometrical phase space or to curtail its to four variables:
• physical substancies (m), including weights (or amounts) of people, animals, plants, foodstuff, weights of products of work (machineries, buildings) and weights of energy and ore resources;
• amount of the information which have been saved up in the system (I): scientific knowledge, social order (political culture, ideology), formation, level of technologies (especially arms). Possible to consider religion, traditions, culture as ideology components. Capital K= m+I.
• expenses per unit of time (year) on manufacture and moving of a physical substacies (dm/dt), and for the speed and adequacy of the information processing (dl/dt). Turnaround actives L = dm/dt + dl/dt.
Physicists apply the definition "phase space" in which together axes of coordinates X, Y, Z and time t as axes of coordinates equal in rights axes of speeds (more precisely pulses) m *dX/dt, m *dY/dy, m *dZ/dt act.
Fig.1. Multidimensional space with axes of coordinates m, I, dm/dt, dl/dt. All specified indicators are expedient for estimating in unified units: money. Thus, the monetary unit is a unit of measure in multidimensional space with axes of coordinates m, I, dm/dt, dl/dt. "Power" of a system can be
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estimated under the formula similar to the formula of Kobb-Douglas
Y = mal Ia2 (dm/dt)a3 (dI/dt)a4 ( 1 )
where al, a2, a3, a4 characterize the importance of factors (elasticities) and if their sum is equal to 1 then Y also has dimension of money.
If dm/dt =0 or dI/dt =0, i.e. the enterprise makes nothing and isn't improve, it costs nothing or will soon depreciate.
Such approach allows to represent the information on social structures in the compressed kind and quickly to make adequate decisions. For example, defeat of the USSR in cold war and its disappearing can be interpreted as follows: the aspiration of the Communist Party to supervise all information space in the state (manufacture and consumption planning, ideology, art, science) has led to small speed of information streams and bad decisions, that is there was a failure in the block (space) dI/dt, then to the structure infringement dm/dt (manufacture, distribution) and ideology disintegration. The state has collapsed, despite of high m, I and dm/dt.
Representations about multidimensional information space, connected with structures in observable space, correlated with traditional views about supernatural powers and their role in a universe. Let's try to formulate definitions of God, Devil, soul:
God is a set of the information (data and algorithms, software), stored in natural objects and promoting arising of objects with the high maintenance of energy and information.
Devil is a set of the information (data and algorithms, software) stored in natural objects and promoting destruction of objects with the high maintenance of energy and information.
Soul is the information about the object, stored as in itself as in other carriers, and influencing processes as in three-dimensional as in information space.
According to the Second Low of Thermodynamics, an entropy of closed system can increase only (a celebration of the Devil), but as in nature as in a society there are objects arise also some time contained high energy and/or high order structures: tornadoes, typhoons, lightnings, gold nuggets, live organisms and biocenoses, people and products of its work, including information (display of God).
Biological systems are steady, if ones aspire to the maximum biomass and a saturation the information (a variety of kinds), i.e. to God; the neglect of people this principle conducts to instability of artificial cultural plants and landscapes with monocultures. On I.V.Prangishvili [1], at management of the organization it should be optimal an order and chaos parity, i.e. a freedom of action for persons, in another case the enterprise will lose in competitive struggle.
To avoid a discussion with clerics, instead of notions of God and of the Devil I suggest to introduce the concepts of G-object, G-process, D-object, D-process. Let's define processes promoting occurrence and existence of objects with the high maintenance of energy and the information as G-processes, and D-processes if on the contrary. Let's define all software stored in natural objects as G-object if
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it supports G-processes in biosphere both social sphere, and D-object if on the contrary.
Laws of as economy as social life operate with the same inevitability, as well as physics laws in spite of the fact that they are shown through activity of people. The people which does not follow the general laws of the nature, disappear, as the animal dies if it ceases to hunt. What are these laws, except usual laws of physics?
1. The Second Low of thermodynamics according to which in a close system energy should dissipate, substances to mix up, chaos to increase. We define these processes as D-processes.
2. In open systems through which takes place a substance and/or energy stream, there can arise and exist local objects with the high maintenance of energy and/or with decrease of the chaos estimated by entropy: tornadoes, typhoons, lightning, gold nuggets, living organisms and ecological communities, people and products of its work, including information. We define processes of their arising and existence as G-processes.
The drawing illustrates a parity of entropy and information in lifeless, biological and social systems, and its evaluation in money (M).
Fig.2. A parity of entropy and information in lifeless, biological and social systems. Arrows show the directions of G-process and arising of M. In the right part of the drawing the parity of entropy and information in biological and social systems is shown:
Zone 1: the entropy is maximum at the absolute chaos, the information equals to zero. An example: the broken and run up army. An estimation of the value of such system by society is zero or negative. In a Zone 1 a decrease of entropy corresponds the increase of the information and a system cost. The direction of G-process and increase in cost of system is from top to down, the D-process direction is from below upwards.
Zone 2 corresponds an information maximum in the system, but entropy is not equals to zero, means, there is no a total order, there is a partial chaos, that is a freedom in choosing. The Zone 2 corresponds to wild ecosystems which aspire to the maximum biomass and a variety. In social systems Zone 2 corresponds a free market and dynamic efficiency realized by free entrepreneurs ordered by laws and morality. They aspire to growth of things and «Хроноэкономика» № 2 (2) сентябрь 2016
the information (including the 9th symphony of Beethoven, Bill Gates Microsoft, etc.) through human entrepreneurial creativity within the limits of public and resource restrictions; also they disappear as businessmen if operate by another way. The mentality of live beings for billions years was generated so that to feel pleasure and happiness at aspiration to a Zone 2 that stimulates instinctive maintenance of dynamic efficiency, that is continuous search and creation of new material and information values, or G-process.
Zone 3: At the total order entropy equals zero, thus the information equals 1 bit, that is almost a zero. An example: army and prison which operate only for supply of their own order; they demand resources, but create nothing. In a Zone 3 decrease of entropy there corresponds the decrease of the information both the system cost. According to the Second Law of Thermodynamics, for maintenance of decrease of entropy, expenses of energy and/or other resources from environment are required, that it is unprofitable doubly. The Zone 3 in biosphere is a zone of agricultural monocultures which can't exist independently. The Zone 3 in social life is a zone of monopolies, collusions, bureaucracy, corruption, interventionism and a Soviet socialism. In micro-economics the Zone 3 corresponds a hierarchical control system that is recognized as unprofitable. A direction of G-process and increase in cost of system is from below upwards, a D-process direction from top to down.
Zone 4: the lifeless nature in which any information is absent, but it is possible to use concept of entropy. Objects with low entropy and the high free energy, arising due to dissipation of huge amounts of Solar or Earth energy, provide people with energy resources (a wind, falling water, fire wood, coal, oil, gas) and separated substances: fresh water, ores, gold. The social importance of these objects estimated in money grows in process of entropy decrease. G-processes are directed from top to down, D-processes are directed from below upwards. Cost of especially pure rare metals with zero entropy is especially great, and they are standards of cost of as lifeless as life objects, including the substantiated and information products of people's work.
The presented principles may be used for esnimatoin of the power of as social as economic systems. We will recognize that biological and social systems aspire to increase in the weight m, information I, and also growth rates of weight (dm/dt) and information processing (dl/dt), that is phase volume, estimated by formula ( 1 ). Increase of Y for animals and plants is limited by the resources accessible to them and extracted in struggle for a survival (dm/dt). The sum of resources, as a rule, is limited and defines biological efficiency of the area. Accumulation and transfer of information to posterity is realized by genes basically, so the speed dI/dt is small. People differ animals. They can extract and use various kinds of lifeless and biological resources, that is increase their value, and also create new material and information values. "Economic restrictions do not arise from objective phenomena and material factors of an external world (for example, oil stocks), but from subjective enterprise knowledge of people" [2, p.37].
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Cooperation plays essential role: material assets and information, coming to the subject of economic activities (actor), initiate manufacture of new material and information values on the basis of available instruments and knowledge. Actor, receiving material and information resources, transfers products to another ones and increases their cost. Therefore manufacture accrues exponentially and is similar to explosion or burning. Explosion or burning begins in one point, at the expense of resource destruction there is an energy escape which initiates energy escape in another points, and avalanche process proceeds, while there are resources. Thus in explosion structures with the high maintenance of energy, essentially influencing a course of process and reducing it forecasting, may be formed. In social and economic systems, due to
interaction of actors, structures with the high maintenance of monetary and information resources are formed: church, government, police, banks, monopolies, criminal communities influencing economic activities of actors. The economic both social process became complicate. These processes look like concentration of energy in turbulent curls.
Referencies
1. Prangishvili I.V. Entropy and other system laws (Entropiinie I drugie sistemnie zakonomernosti) / Moscow, Science, 2003.
2. J. Huerta de Soto. The theory of dynamic efficiency. (Socialno-ekonomicheskaia teoria dinamicheskoi effektivnosti) / Moscow, Socium, 2011.
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