Wednesday, September 3, 2014

Insights from non-ideal information transfer in physical processes

In addition to the discussions about the source of information in a transfer process, Peter Fielitz provided a great insight into how non-ideal information transfer manifests itself through an analogy with a real gas (as opposed to an ideal gas). In the graph below, I plot a schematic path followed by a real gas in an isothermal compression/expansion on a p-V diagram in blue:

The ideal gas behavior p = (2/f) (E/V) is given by the dashed line; this is the expected path followed with ideal information transfer, I(E) = I(V). We see the pressure is p ≤ (2/f) (E/V) if we are at the blue point near the gas-liquid transition.

There are a couple of interesting analogies [1] to be gleaned from this:
  • Peter pointed out that as V→∞, the information transfer becomes ideal and  I(V) ≈ I(E). We would imagine that given approximately constant demand D, information transfer in an economic process if not already ideal would become ideal as the supply S becomes sufficiently large. This is an interesting result because it implies that sufficiently large markets should behave like an ideal information transfer process.
  • The reason that the blue curve deviates from the dashed curve is primarily attractive forces between molecules (which eventually cause the gas to condense into a liquid). This would be analogous to the details of a micro-economic theory ("microfoundations", e.g. agent based models, DSGE models) causing the market to deviate from ideal information transfer, resulting in I(S) < I(D). Coupled with the previous point, we could expect the effect of the microfoundations to vanish in a sufficiently large economy (S→∞) as we approach I(S) ≈ I(D).

[1] We must always remember to keep Samuelson in the back of our minds when looking at analogies between physics and economics:
There is really nothing more pathetic than to have an economist or a retired engineer try to force analogies between the concepts of physics and the concepts of economics. How many dreary papers have I had to referee in which the author is looking for something that corresponds to entropy or to one or another form of energy.
The formal mathematical analogy between classical thermodynamics and mathematical economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes -- such as entropy or energy -- in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should 'utility' be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?

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