Entropy and Gravity in Economics (draft)

NOTICE

• DO NOT TRUST THE FOLLOWING

Perspective

• There's two basic extensive quantities in thermodynamics: energy and entropy
• In economics, analogy between energy and wealth was well acquainted (See Mirowski's More Heat than Light)
• When free energy (thermodynamic potential) goes to zero limit, total energy is maximum
• When marginal utility (economic potential) goes to zero limit, integrated total utility is maximum
• Gibbs-Fisher-Le Chatelier-Samuelson's thermodynamical economics is more or less explicitly built on this analogy
• Another analogy between entropy and demand was not so widely nor explicitly thought
• And underlying principle for origin of "gravity" between goods and people is still left unaccounted

Entropy

• Probably the most radical Samuelsonian was Nicholas Georgescu-Roegen
• His view was a revival of "limit of growth as steady state" concepts, like Ricardo's and Marx' "rate of profit to fall" arguments or Ramsey's "bliss", in the form of Boltzmann's thermodynamical apocalypse, "heat death"
• In his view, a notorious example in a DOSSO footnote is indeed the "breakdown of capitalism" (Georgescu-Roegen(1960))
• He was too radical to be understood seriously and economics is kept unchanged after him

Gravity

• Timbergen's gravity model is standard equipment in international economics

TODO

• refer entropic gravity, relativity and quantum gravity
• asymptotic extensivity of von Neumann entropy and determinant

Towards Justificaton of Say's Law (preliminary)

NOTICE

• NEVER TRUST THE FOLLOWING

Summery

• Principal axiom of classical economics: Say's law (S = D)
• Neo-classical generalization: Walras' law ($\Sigma{ps} = \Sigma{pd}$)
• Supply might be estimated as total wealth (in equilibrium theories, assumed somewhat constant, except on unpredictable changes of tastes and technologies)
• Demand might be formulated as utility function (might be usually function of price of goods, expectation, with any other endogeous parameters)
• Usually, tangible affections (shocks to technologies and tastes) to equilibrium is usually formulated in supply function, and demand is determined with markets alone
• Note that: Technology seems to be supply factor, but tastes are not supply factor for non-economists

Supply - Wealth - Exchange Value - Demand - Welfare - Utility - Use Value

• If you think all these words above have same meaning, you need only one word
• We use such words vaguely but quite differently
• These must not be confused each other
• And indeed Say's (Walras') law need theoretical justification

TODO

• State an acceptable definition for demand