Dynamical Economic model in a finite world
Christophe Goupil1, Eric Herbert1, Yves D'Angelo1, Quentin Couix2
1DyCoE Team, Laboratoire des Energies de Demain, LIED, UMR 8236, Université Paris Diderot
2 Université Paris Sorbonne
Ecoles des Houches 10 mars 2016
[email protected]
Including, or not, the ressources
Perpetual motion et al...
Glucina et al. 2010
Hall et al. 1986
Berg et al. 2015
Economics
• What do we learn from mechanics?
• What do we learn from equilibrium thermodynamics?
• What do we learn from out of equilibrium thermodynamics?
• Does economics have something to do with thermodynamics?
• A model where few things matter: (conservation, friction, rate…)
Economics IS Mechanics!...............?
… and Herman Laurent wrote to Léon Walras….
(about the integrability of the model)
Economics ARE Thermodynamics !............?
Equilibrium thermodynamics: Callen approach
General structure
Thermodynamics
Economics
Thermoelastic coefficients & Elasticities
Is there an Economic “material”?
Debreu: Job is done….Really?
So, in other words:
The economics "material" is defined by the laws acting on...the economic "material“
The economics laws are derived from the measurements made on the economics
“material”… which is defined by the same laws…that define….
Partial conclusion
1. Economics do not have the structure of thermodynamics.
2. There is no problem with doing local optimization…until we don’t claim it is GENERAL.
3. There is no fundamental equation for the economy, nor variational principle (hopefully)
4. There is no ergodicity.
5. T, P…are emerging properties, are there any in economics?
GENERAL EQUILIBRIUM
And….Economic systems are not equilibrium systems!
Commodity space
Out of equilibrium: Schumpeter
The Roegen assumption: « matter matters too»
The far out of equilibrium
assumption is ok,
but
there is no need of a fourth
thermodynamics principle
for matter.
Money temperature (Yakovenko 2009)
There is no problem with such
a definition, but why should
we call it temperature and not
simply the average value of
the money carried by agents?
AND!
There is no emerging quantity
« Well-lit roads and burned bridges » (Glucina & Mayumi 2010)
"The fact that there are no known exceptions to the laws of thermodynamics should be
incorporated into the axiomatic foundation of economics."(Underwood 1989) ∙
"Real financial markets cannot behave thermodynamically" because "financial markets are
unstable, they do not approach statistical equilibrium, nor are there any available topological
invariants on which to base a purely formal statistical mechanics." (Mc Caulley 2003) ∙
"If economics is to be considered as a science-based discipline, the principles of physical
science, including the laws of thermodynamics, must be appropriately applied." (Wallace 2009)
"We need to begin to incorporate energy and entropy thinking into economics."(Kummel 2011)
The use of thermodynamics in Economics
• Conservative laws (no full substitutability)
• Non conservation of some physical quantities (utility...)
• Difference between extensive and intensive physical quantities
• Intensive physical quantities are the potentials from which we can derive forces∙
• Intensive physical quantities are the potentials that give a possible measurement of the quality∙
• There is no economic entropy but we can consider quantity and quality approach∙ (general exergy)
• Give up the full thermodynamic paradigm (Integrability, Equation of state...)
• Time does matter BUT, there is no variational principle in out-of-equilibrium systems
Time does matter: a mechanical description
(Odum & Pinkerton 1955)
(Hall 1994)
Efficiency is not restricted to pure thermodynamic description.
Odum-Pinkerton, Yvon, Chambadal, Novikov, Curzon & Ahlborn
Thot
Thot
Finite Time
Thermodynamics
FTT
Work
Power
Endoreversible
Tcold
Tcold
P
Tcold
W
C 
 1
Qin
Thot

Pmax
Tcold
CA    1 
Thot
Q in
W
ηCA
ηCarnot
• J. Yvon, The saclay Reactor: Two Years of Experience in the Use of a Compresed gas as a Heat Transfer Agent,
Proceedings of the International Conference on the Peaceful Uses of Atomic Energy (1955)
• P. Chambadal Les centrales nucléaires. Armand Colin, Paris, France, 4 1-58, (1957)
• I.I. Novikov, Efficiency of an Atomic Power Generation Installation, Atomic Energy 3 (1957)
• F.L. Curzon & B. Ahlborn, Efficiency of a Carnot Engine at Maximum Power Output, Am. J. Phys. 43 (1975)
• For a review, see Ouerdane et al.., Eur. Phys. J. Special Topics 224, 839–864 (2015)
η
The position of the point on
the curve is defined by the
intensity parameter which
governs the output.
Efficiency or Power?
Irreversibilities included
 Friction
 Leak: natural degradation
Low friction
Source
PR
PPH
High friction
Output
DP
Carnot
« More is not always better »
FPH
Production
PPL
FPH
PS
Sink
Goupil et al. 2012
Efficiency or power : (small DP change)
friction
restricted access
to ressources
leak
friction + leak
friction + leak+ restricted access to ressources
The Lego brick
Hall et al. 2006
The Lego brick description
Internal parameters:
 Total ressource XT
 Frictions: R
 Coupling terms: a
 Natural recycling: FNR
M=Rin/Rload
Inputs: demands
 Production (Leontief PC)
 Recycling (Leontief PR)
 Prod output: WPCout
 Recycling flux
…
 Healt parameter: M
1 Safe: M>>1

2
Outputs:
3
1
4

2 Max Eff: M=(1+Z)0.5

3 Max Prod: M=1

4 Unsafe: M<1
Complete system
Complete system (small DP change)
M2
M1
K
Smell test…
Smell test: recycling increased
Conclusions
1.
2.
3.
4.
5.
Economics do not have the structure of thermodynamics.
There is no economic entropy but quantity and quality approaches are possible
There is no fundamental equation for economy (hopefully)
There is no ergodicity.
Economic system are not equilibrium systems.
There is no problem with doing local optimization…until we don’t claim it is GENERAL.
1.
2.
3.
4.
5.
6.
Conservative laws (non full substitutable)
Non conservation of some physical quantities (utility...)
Difference between extensive and intensive physical quantities
Intensive physical quantities are the potentials from which we can derive forces
Give up the full thermodynamic paradigm (Integrability, Equation of state...)
Time does matter BUT, there is no variational principle in out of equilibrium systems
References
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Walras 1909: Walras Léon Économique et Mécanique, Bulletin de la Société Vaudoise de Sciences Naturelles Vol. 45, p.313-3251.
Soddy 1911: Soddy, Frederick. (1911). Matter and Energy (pgs. 33-35). H. Holt and Co.
Soddy 1920: Soddy, Frederick. (1920). Science and Life, New York: Dutton.
Soddy 1921: Soddy, Frederick. (1921). "Cartesian Economics: the Bearing of Physical Science upon Start Stewardship“.
Wilson 1938: Wilson, Edwin. (1938). "Letter to Paul Samuelson", Dec 30.
Gibbs 1876: Willard Gibbs, (1876): "Internal Stability of Homogeneous Fluids as indicated by Fundamental Equations“
Samuelson 1947: Samuelson P. A . (1947), Foundation of Economic Analysis (Cambridge, MA, Harvard University Press)
Samuelson 1960: Samuelson, Paul A. (1960). "Structure of a minimum equilibrium system“
Debreu 1984: G. Debreu, Théorie de la valeur. Une analyse axiomatique de l'équilibre économique, Paris, Dunod, 1984
Schumpeter 1939: Business Cycles: A Theoretical, Historical and Statistical Analysis of the Capitalist Process, 1939
Yakovenko 2009: Victor M. Yakovenko and J. Barkley Rosser, Jour. Rev. Mod. Phys. 81, 1703.
Roegen 1971: Georgescu-Roegen, Nicholas. (1971). The Entropy Law and the Economic Process. Cambridge, Massachusetts.
Ayres 1999: Robert Ayres, The second law, the fourth law, recycling and limits to growth , Ecological Economics, vol. 29, n° 3, p. 473-483
Underwood 1989: Underwood, D. A. and King, P. G. (1989). "On the Ideological Found. of Environ. Policy", Ecological Economics 1: 324
Mc Cauley 2003: McCauley, Joseph L. (2003). "Thermo. Analogies in Eco. and Finance…" Physica A, 329 (2003): 199-212.
Wallace 2009: Wallace, Thomas P. (2009). the Dynamics of Decaying Civilizations from Ancient Greece to America (pg. 31). AuthorHouse.
Kummel 2011: Kummel, Reiner. (2011). The Second Law of Economics: Energy, Entropy, and the Origins of Wealth.
Lotka 1922: A.J.Lotka (1922) 'Contribution to the energetics of evolution'. Proc Natl Acad Sci, 8.
Odum 1955: H.T.Odum and R.C.Pinkerton (1955) 'Time's speed regulator….”, Am. Sci., 43 pp. 331—343
Out of equilibrium thermodynamics references
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H. Ouerdane, Y. Apertet, C. Goupil, and Ph. Lecoeur, Continuity and boundary conditions in thermodynamics: From Carnot’s efficiency to
efficiencies at maximum power ,Eur. Phys. J. Special Topics 224, 839-864 (2015)
H. Ouerdane, A. A. Varlamov, A. V. Kavokin, C. Goupil, and C. B. Vining, Enhanced thermoelectric coupling near electronic phase
transition: the rôle of fluctuation Cooper pairs, Physical Review B 91, 100501 (R) (2015)
Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Influence of thermal environment on optimal working conditions of thermoelectric
generators, J. Appl. Phys. 116, 144901 (2014)
Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, On the distinction between maximum power and maximum efficiency working
conditions for thermoelectric generators, Journal of Applied Physics 116, 144901 (2014)
Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Efficiency at maximum power of thermally coupled heat engines, Physical Review E
vol. 85, 041144 (2012)
Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Irreversibilities and efficiency at maximum power of heat engines: The illustrative
case of a thermoelectric generator, Physical Review E vol. 85, 031116 (2012)
Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Thermoelectric internal current loops inside inhomogeneous systems, Physical
Review B vol. 85, 033201 (2012).
Y. Apertet, H. Ouerdane, O. Glavatskaya, C. Goupil and Ph. Lecoeur, Optimal working conditions for thermoelectric generators with
realistic thermal coupling, Europhysics Letters vol. 97, 28001 (2012)
Utility: Locally ok but is global optimization possible?
The integrability question
Ut
Neoclassical Economy
“According to the feasibility study, it is feasible, but,
According to the idiotability studies it is absolutely idiot.”