C. Udriste, M. Ferrara, D. Zugravescu, F. Munteanu

Abstract

Section 1 presents a connection between geobiodynamics and the Roegen type economy. Section 1 discusses the applicability of concepts and techniques of thermodynamics in economics and viceversa via an isomorphism. Section 2 shows that the economy of European Union Economy is far form equilibrium. Section 3 describes some economic black holes as small parts of a global economic system in which the national income is so powerful. We use these ideas to improve our understanding of the nature of thermodynamic-economic development and evolution.

Mathematics Subject Classification: 80A99, 91B74 J.E.L. classification: B41

Key words: Key words: Roegen economy, thermodynamics-economics dictionary, economic black holes, economic equilibrium.

1   Geobiodynamics and Roegen Type Economy

The Planet Earth System, is, as any living system (or system supporting life), extremely difficult to define and characterize properly and completely. Presently mankind can be described as being in a Modern Era in which the Informational Society is currently unfolding while at the same time the Knowledge-based Society (while not fully matured or functional) may be re­garded as emerging. Taking into account this general context, we attempt a definition of the Planet Earth System that extends beyond the natural struc­tures (inorganic, organic or living) that are typically the object of study for

Geosciences and/or Biology and Biochemistry. However, besides the Natural structures, man-made Artifacts have also been produced throughout the en­tire human history and, after adding onto/combining with the Natural ones, resulted in a complex symbiot. Presently, a tentative list of such artificial systems with significant impact (ecologically, economically and socially) may include the following items:

–  the entire assembly of systems dedicated to the generation and distri­bution of electrical energy, as well as the extraction and refinement of oil and the distribution of the final oil-derived products down to industrial and individual customers;

–  the entire combination of roadways, rail-roads and airways that make up the infrastructure necessary for commerce and tourism, i.e. the circulation of goods and people;

–  the production and distribution of any type of goods.

All these Artificial systems, when combined with the Natural ones in which they are situated and/or with which they interact for their normal operation generate an entirely new System, of a different type and qual­ity. Natural and Artificial systems are now intermingled, interacting, inter­related and interdependent, thus permanently defining and influencing each other, giving rise to an entirely new and qualitatively different dynamics. This novel symbiosis and its dynamics are only partly controllable or pre­dictable, and in order to be understood (even if only partially) they have to be examined using an interdisciplinary approach, a re-evaluation of the classical sciences, a fundamental change in the points of views and techniques used to study, model and predict such complex systems [3].

Investigations have been started and research is being carried out world­wide in order to elucidate which are the best directions of study to be fol­lowed for the examination and understanding of this Artificial-Natural hy­brid. From the findings that have resulted from such work until now it is worth mentioning that ‘the sole methodology capable to study an object of such a complexity and diversity with an integrative approach is that offered by the Science of the Complexity’ [14]. In this new vision, the behavior and dynamics of the Planet Earth System is simultaneously determined by two major force systems:

a) The complicated interactions between the crust, atmosphere, hydro­sphere and ionosphere, whose activity is additionally influenced and mod­ulated by the Solar System’s dynamics (electromagnetic storms, the solar

‘wind’, the ionospheric and telluric currents, the sun spots and their erup­tions, the tides, etc.)

b) The essential social components that define in their evolution new needs and opportunities, resulting in a constantly changing world of arti­facts, and hence a permanently modifying coupling and interaction between Natural and the Artificial across the entire planet.

From this perspective, the sociological, economical or engineering stud­ies/sciences must be reconfigured and integrated in a larger and broader subject (meta-science) that transcends yet combines them interdisciplinary in order to create this new framework in which each part would also depend on and be supported by elements from the other ones. In a first stage, the generation and application into practice of the previously mentioned phe­nomenon has already been started as an increasing number of researchers more and more frequently refer to such novel meta-domains, e.g. bioecon-omy, biogeophyisics, geobiophyisics, astrobiophyisics as well as bioelectronics, microelectromechanics and jurisdynamics. Although not yet fully mature or developed as complete meta-sciences, we can still consider them as interme­diary stages in the integration of several different sciences in a new area. We can thus presume that this can be identified as the first sign highlighting a significant current trend of integration of various disciplines that ultimately may lead towards a single global concept, probably similar to some extent with the Gaia concept [4,5]. It should be clear that, once such a meta-science has been generated, disciplines like economics and sociology will no longer be studied separately or independently, but interdependently and always within the context of their interactive co-evolution with the Planet Earth System.

Consequently, in this new context one may expect increased interest and more intense studies in the following possible directions: (1) stimulat­ing knowledge transfer between different fields and encouraging pluri- and inter-disciplinary approaches; (2) evaluating the capability of present day’s methodologies of efficiently understanding theoretically and experimentally the transition from part to the whole, from complicated to complex; (3) dis­covering or inventing new experimental concepts, models, theories, methods and techniques of monitoring and evaluating hierarchical dissipative systems that evolve far from thermodynamical equilibrium; (4) developing and suc­cessfully using an educational infrastructure that can ensure the transfer and filtration of information and specific knowledge and know-how.

The main target is to educate the new generation and re-educate the cur­rent one by shifting from the current reductionist paradigm to one related to nonlinearity and complexity. This should result in a better understand­ing of current phenomena, increased capacity and willingness to assimilate new knowledge and adopt an exploratory frame of mind in order to further generate new knowledge. Therefore, a long-term consequence of such a new educational infrastructure should be the creation and propagation through society of a life-long learning attitude, based on a formal ‘standard’ education but also including an informal one and a non-formal one as well, while at the same encompassing both localized and delocalized aspects (e.g. e-learning).

WIKIPEDIA: “Nicholas Georgescu-Roegen, born Nicolae Georgescu (Ro­mania, Constanta, Romania, 4 February 1906; Nashville, Tennessee, 30 Oc­tober 1994) was a Romanian mathematician, statistician and economist, best known for his 1971 magnum opus [2], which situated the view that the second law of thermodynamics, i.e., that usable “free energy” tends to disperse or become lost in the form of “bound energy”, governs economic processes. His book is considered a founding book in the field of thermoeconomics.”

Roegen introduced into economics the concept of entropy from thermo­dynamics and did foundational work which later developed into evolutionary economics. Also his work contributed significantly to bioeconomics and to ecological economics.

In this paper we explore the vision of Nicolae Gergescu Roegen, who re­lated the economical phenomena to entropy [5]. For this purpose we identify a formal correspondence between economic processes and thermodynamic laws, with heuristic implications for characterizing the dynamics and evo­lution of economical systems. Based on this formalism we then study the problem of establishing an economical equilibrium in the case of aggregating together initially stable and independent economical subsystems in a final functional entity, e.g. the set up of the European Community’s economy. Similarly, we intend to extend the physics’ black hole concept in order to apply it in economy as well. This would be possible by applying to eco­nomical phenomena the formalism usually used to model entropic processes. In order to apply successfully such formalism a Thermodynamics-Economics Dictionary would be created, as a clear Table of correspondences between physical parameters and economical ones. This Dictionary/Table would be just one of the dedicated tools and examples proposed in this paper illustrat­ing the capacity of transferring and utilizing knowledge and theories from one initial, well-defined and established, field (physics, in this case) into the understanding and modeling of another one (economical processes).

2   Thermodynamics-Economics Dictionary

The thermodynamics is important as a model of a phenomenological theory, one which describes and unifies certain properties of many different sorts of physical systems. There are many systems in biology, economics, and com­puter science, for which a similar organizing and unifying phenomenological theory would be highly desirable. Our aim is to present certain features of economics inspired from thermodynamics and viceversa, giving a short dictionary that reflect the Thermodynamics-Economics isomorphism.

The formal analytical-mathematical analogy between economics and ther­modynamics is by now fairly well-known or at least accepted by economists and physicists alike [1]-[14]. In this context, the papers [8]-[13] build an isomorphism between thermodynamics and economics, admitting that the fundamental laws are also in correspondence via our identification. In this way each thermodynamic system is naturally equivalent to an economic sys­tem, and the laws in thermodynamics have correspondents in economics.

3   Equilibrium of European Union Economy

The European Union (EU) is a union of twenty-seven independent states based on the European Communities and founded to enhance political, eco­nomic and social co-operation. Therefore we must analyze the equilibrium states after interaction of 27 simple economic systems:

R⁵, u_i = dGi – IidEi + PidQi = 0, i =1,27.

The evolution of each simple economic system can be only 1-dimensional or 2-dimensional manifolds since each 1-form u_i is a contact form.

The best way to analyze the interaction is to consider the product eco­nomic system

R¹³⁵, u_i = 0, i = 1,…, 27

and to look for the constrained critical points of some suitable functions.

Geometrically, the set of all critical points is a hyperplane in R¹³⁵. Eco­nomically, the equilibrium of interacting economic systems can be realized only for “equal internal politic stabilities” and “equal level of prices (infla­tion)”. Consequently the nonequilibrium in European Community is math­ematically obvious and our Gibbs-Pfaff economic models are sustainable.

4   Economic Black Holes

From WIKIPEDIA: “A black hole is a region of space in which the gravita­tional field is so powerful that nothing can escape after having fallen past the event horizon. The name comes from the fact that even electromagnetic radiation (e.g. light) is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. While the idea of an object with gravity strong enough to prevent light from escaping was proposed in the 18th century, black holes as presently understood are described by Einstein’s theory of general relativity, developed in 1916. This theory predicts that when a large enough amount of mass is present within a sufficiently small region of space, all universal lines from the space are warped inwards towards the center of the volume, forcing all matter and radiation to fall inward. While general relativity describes a black hole as a region of empty space with a pointlike singularity (gravitational singularity) at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research on this subject indicates that, rather than holding captured matter forever, black holes may slowly leak a form of thermal energy called Hawking radiation. However, the final, correct description of black holes, requiring a theory of quantum gravity, is unknown.”

Similarly an economic black hole is a small part of global economic system in which the national income is so powerful that nothing can escape after having falling past the event horizon. It is described in terms of the entropy E, the national income (revenue) Y, the total investment I and the economic spin J [11]. Of course, these models are different from what is called usually “Economic Black Holes”.

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