Geobiodynamics and Roegenian Economic Systems (1812.07961v1)
Abstract: This mathematical essay brings together ideas from Economics, Geobiodynamics and Thermodynamics. Its purpose is to obtain real models of complex evolutionary systems. More specifically, the essay defines Roegenian Economy and links Geobiodynamics and Roegenian Economy. In this context, we discuss the isomorphism between the concepts and techniques of Thermodynamics and Economics. Then we describe a Roegenian economic system like a Carnot group. After we analyse the phase equilibrium for two heterogeneous economic systems. The European Union Economics appears like Cartesian product of Roegenian economic systems and its Balance is analysed in details. A Section at the end describes the "economic black holes" as small parts of a a global economic system in which national income is so great that it causes others poor enrichment. These ideas can be used to improve our knowledge and understanding of the nature of development and evolution of thermodynamic-economic systems.
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Conceptual Simplification
Plain-language summary of the paper’s core contributions
Why bring thermodynamics into economics?
The paper builds on Nicholas Georgescu-Roegen’s idea that economic activity, like physical processes, is constrained by “entropy” and evolves under forces and flows. The authors formalize this idea: they construct a one-to-one “dictionary” that maps key thermodynamic quantities and laws to economic counterparts, then use that mapping to analyze equilibrium, dynamics, and extreme phenomena (like “black holes”) in an economic setting.
To make the analogy concrete, they propose a few intuitive correspondences (examples):
- Temperature ↔ internal political stability (how smoothly the system can operate)
- Pressure ↔ price level/inflation (how “tight” markets feel)
- Volume ↔ quantity/quality/structure of output
- Internal energy ↔ growth potential
- Entropy (S) ↔ economic entropy (E), a measure tied to dispersion/irreversibility in the system
A single constraint that ties the economy together
At the heart of their framework is an economic version of a thermodynamic identity (the Gibbs-Pfaff equation):
- Economic constraint: dG − I dE + P dQ = 0
- G = growth potential,
- I = internal political stability (intensive),
- E = economic entropy (extensive),
- P = price level (intensive),
- Q = output/quantity/structure (extensive).
Intuition: any small change in the economy must balance these three pieces—changes in potential growth, stability/entropy, and price/quantity—just as heat, work, and energy balance in thermodynamics. The authors call an economy governed by this constraint a “Roegenian economy.”
From this foundation, they state three “economic laws,” parallel to the thermodynamic ones:
- First law (bookkeeping of change): dG = I dE − P dq
- Second law (entropy doesn’t fall in isolation): dE ≥ 0 for an isolated economy
- Third law (breakdown under zero stability): if I → 0, then E → 0 (the system “freezes”)
These laws distinguish “forces” (intensive, like I and P) from “flows” (extensive, like E and Q), and say imbalances in forces cause compensating flows.
Path-dependence and “order matters”: a Carnot-group view
The paper shows that when you combine policy moves or market changes, the order you apply them in matters for where the system ends up—this is path dependence. Mathematically, they model this with a structure where addition is not always commutative (“A then B” differs from “B then A”). You can think of this as formalizing the intuition that the sequence of reforms, shocks, or investments changes outcomes.
They then build a geometry around the basic constraint (think: the economy can only move along directions that respect dG − I dE + P dQ = 0). Within this geometry they compute “shortest” or “most efficient” paths under the constraint (geodesics). Intuitively, those are the lowest-effort combinations of policy and market adjustments to move the system from A to B without breaking the structural balance.
Equilibrium for two intertwined “phases”: goods and money
Borrowing the idea of “phase equilibrium” from thermodynamics, they analyze an isolated economy with two interdependent parts (phases): commodities and money. The key message is simple:
- At equilibrium, internal political stability and price levels must be equal across the two phases:
- I₁ = I₂ and P₁ = P₂
The authors also identify a Gibbs-like “economic potential” per unit of value,
- p = g + P q − I e, and show that at equilibrium this potential must match across phases (p₁ = p₂). This is an economic counterpart of equalizing potentials in thermodynamic phase equilibrium. Conceptually, it’s an elegant way to capture “no-arbitrage” conditions between the money side and the goods side.
They also point out that thinking in terms of a “phase diagram” naturally suggests a “triple point” for an economy—where three regimes (or “phases”) can coexist.
The European Union as a multi-economy system: what “utopian” equilibrium would require
The authors model the EU as the product of 27 Roegenian economies, each satisfying the basic constraint. They then ask: what do the classical equilibrium conditions imply when these economies interact?
Using a constrained optimization approach (Lagrange multipliers), they show that a perfectly balanced, “utopian” equilibrium across members would require:
- equal internal political stability across countries, and
- equal price levels (inflation) across countries.
Because that’s unrealistic, they propose a practical relaxation: use weighted averages for aggregate objectives (growth, entropy, output). With weights reflecting policy priorities or structural differences, the equilibrium requires equality of weighted aggregates instead of raw equality. Intuitively, this is a way to define “harmonization” instead of “uniformity,” closer to how real unions coordinate.
“Economic black holes”: regions that draw in resources
Extending another thermodynamic concept, the paper defines “economic 3D black holes” as parts of the global economy whose income is so strong that they pull in surrounding resources and activity. Through their dictionary, standard black-hole formulas translate into economic relationships between:
- E (entropy), Y (national income), I (investment), and J (an “economic spin” capturing rotational/asymmetric effects).
They give three model types—analogues of Reissner–Nordström, Kerr, and BTZ black holes—each yielding threshold-like inequalities (e.g., Y ≥ I or Y ≥ √J). Intuitively, these bounds describe when a region’s income is high enough to generate a “gravitational” pull on capital, labor, and trade.
The open question they pose is to interpret such inequalities economically—for example, what does Y ≥ √J mean in terms of concentration, network effects, or systemic dominance?
Why this matters
- It unifies a number of macroeconomic behaviors—equilibrium, adjustment paths, and extremes—under one constraint that is easy to interpret.
- It provides ready-made tools: once the dictionary is accepted, well-developed thermodynamic and geometric methods become available to paper economic stability, transitions, and policy trade-offs.
- It highlights path dependence: the sequence of policy moves can be as important as their totals.
- It offers a clean way to think about multi-region balances (like the EU), distinguishing idealized uniformity from realistic, weighted harmonization.
Main takeaways in one place
- A clear thermodynamics-to-economics dictionary ties forces, flows, and potentials across domains.
- A single constraint, dG − I dE + P dQ = 0, encodes how economic quantities must co-move.
- Equilibrium in mixed systems requires equalization of intensive variables (stability and prices) and of a Gibbs-like economic potential.
- For unions of economies, perfect equilibrium implies equal stability and prices; a weighted version provides a more realistic coordination target.
- “Economic black holes” formalize the idea of dominant regions that absorb resources, yielding threshold conditions worth interpreting and testing.
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