Dynamical Economic model in a finite world Christophe Goupil 1, Eric Herbert 1, Yves D'Angelo 1, Quentin Couix 2 1

Transcription

1 Dynamical Economic model in a finite world Christophe Goupil 1, Eric Herbert 1, Yves D'Angelo 1, Quentin Couix 2 1 DyCoE Team, Laboratoire des Energies de Demain, LIED, UMR 8236, Université Paris Diderot 2 Université Paris Sorbonne Ecoles des Houches 10 mars 2016 christophe.goupil@univ-paris-diderot.fr

2 Including, or not, the ressources Perpetual motion et al... Glucina et al Hall et al Berg et al. 2015

3 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 )

4 Economics IS Mechanics!...? and Herman Laurent wrote to Léon Walras. (about the integrability of the model)

5 Economics ARE Thermodynamics!...?

6 Equilibrium thermodynamics: Callen approach

7 General structure

8 Thermodynamics

9 Economics

10 Thermoelastic coefficients & Elasticities Is there an Economic material?

11 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.

12 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? Commodity space GENERAL EQUILIBRIUM And.Economic systems are not equilibrium systems!

13 Out of equilibrium: Schumpeter

14 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.

15 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

16 «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)

17 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

18 Time does matter: a mechanical description (Odum & Pinkerton 1955) (Hall 1994) Efficiency is not restricted to pure thermodynamic description.

19 Odum-Pinkerton, Yvon, Chambadal, Novikov, Curzon & Ahlborn T hot Work Finite Time Thermodynamics FTT T hot Power Endoreversible T cold T cold C W 1 Q in T T cold hot P P max η CA η Carnot η CA W Q in 1 T T cold hot 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, , (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, (2015) The position of the point on the curve is defined by the intensity parameter which governs the output.

20 Efficiency or Power? Irreversibilities included Friction Leak: natural degradation Low friction Source P R High friction DP P PH Production F PH Output Carnot P PL F PH «More is not always better» P S Sink Goupil et al. 2012

21 Efficiency or power : (small DP change) friction leak friction + leak restricted access to ressources friction + leak+ restricted access to ressources

22 Hall et al The Lego brick

23 The Lego brick description Internal parameters: Total ressource X T Frictions: R Coupling terms: a Natural recycling: F NR M=R in /R load Inputs: demands Production (Leontief PC) Recycling (Leontief PR) Outputs: Prod output: W PCout Recycling flux Safe: M>>1 2 Max Eff: M=(1+Z) 0.5 Max Prod: M=1 3 Unsafe: M<1 4 Healt parameter: M

24 Complete system

25 Complete system (small DP change) M 2 M 1 K

26 Smell test

27 Smell test: recycling increased

28 Conclusions 1. Economics do not have the structure of thermodynamics. 2. There is no economic entropy but quantity and quality approaches are possible 3. There is no fundamental equation for economy (hopefully) 4. There is no ergodicity. 5. Economic system are not equilibrium systems. There is no problem with doing local optimization until we don t claim it is GENERAL. 1. Conservative laws (non full substitutable) 2. Non conservation of some physical quantities (utility...) 3. Difference between extensive and intensive physical quantities 4. Intensive physical quantities are the potentials from which we can derive forces 5. Give up the full thermodynamic paradigm (Integrability, Equation of state...) 6. Time does matter BUT, there is no variational principle in out of equilibrium systems

29 References Walras 1909: Walras Léon Économique et Mécanique, Bulletin de la Société Vaudoise de Sciences Naturelles Vol. 45, p Soddy 1911: Soddy, Frederick. (1911). Matter and Energy (pgs ). 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, 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 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): 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

30 Out of equilibrium thermodynamics references 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, (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, (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, (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, (2014) Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Efficiency at maximum power of thermally coupled heat engines, Physical Review E vol. 85, (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, (2012) Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Thermoelectric internal current loops inside inhomogeneous systems, Physical Review B vol. 85, (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, (2012)

31 Utility: Locally ok but is global optimization possible? U t The integrability question

32 Neoclassical Economy According to the feasibility study, it is feasible, but, According to the idiotability studies it is absolutely idiot.