Re: zero average profit

From: Philip Dunn (pscumnud@DIRCON.CO.UK)
Date: Wed Jun 11 2003 - 11:50:22 EDT

```Quoting Ian Wright <ian_paul_wright@HOTMAIL.COM>:

> Hello Philip,
>
> I follow Duncan Foley's work quite closely, primarily because I
> think it is top notch. I tried to apply the approach he outlined
> in his paper, "A statistical equilibrium theory of markets" to the
> analytical analysis of my computational model, but found it too
> difficult, and instead I got away with something simpler, which
> was sufficient for my purposes.
>
> I must admit to not realising there is an important difference
> between thermodynamics and statistical mechanics (I perhaps
> erroneously lump it all together as statistical physics). I do not
> know what reversible near-equilibrium changes are.

Hello Ian

The difference is that thermodynamics is not statistical, it is deterministic.
There can be a thermodynical limit of statistical mechanics.  Measured at
picosecond intervals the pressure of a gas, at any gien point, will fluctuate
markedly.  If, however, the ergodic hypothesis of Boltzmann applies then this
flucuating pressure will quickly time-average towards the 'ensemble' average
(the volume average of pressure at a given time). Then you can do thermodynamics.

If you let a hot cup of tea cool, that's an irreversible change. Initially the
tea was out of equilibrium with its surroundings. The loss of entropy by the
tea, (-delta Q)/T(high) where delta Q is the heat transferred in a short
interval, is less than the gain of entropy by the surroundings, (+delta
Q)/T(low). Entropy has increaed overall (second law of thermodynamics).

The change is reversible when entropy does not increase overall. This means
staying very close to thermal equilibrium with the surroundings during the
change, or staying isolated from the surroundings.

In Duncan Foley's paper Walrasion adjustment from initial endowments to
equilibrium is irreversible. To quote: "Economic utility corresponds precisely
to that component of thermodynamic entropy whose change arises from irreversible
transformations".

>
> It's not a drawback that econophysics raises questions
> about possibile similarities between different systems (if this is
> your implication). Of course there are always specific differences,
> but I think that self-similarity of nature at all scales is ubiquitous,
> which is one explanation for the universality of much of
> mathematics, and even a rationale for the utility of scientific
> analogies.

I do not see it as a drawback. I simply do not know what the correspondences are
for Marxian economics. One problem is that economies do not seem to exhibit much
in the way of ergodicity. Without that there can be no deterministic
thermodynamic limit.

>
> In my own work I found that at the equilibrium of a simple
> commodity economy the price distributions for different
> commodities have "temperatures" given by the monetary
> expression of labour time (M) multiplied by the labour value
> (L) of the commodity. That is, the probability of commodity
> i realising price k is given by:
> P(k)=(1/ML) * exp(-k/ML)
> The expectation of the price variate is simply ML, which is the
> average price of the commodity, and analogously the
> commodity's "temperature". In this case the average price
> is linearly proportional to the labour time necessary
> for the commodity's production. All the commodities in the
> system share the MEL, as the sectors are in statistical equilibrium,
> but are weighted by their interaction times, which are the
> sectoral labour values (longer production times, lower interaction
> frequencies). Situations in which different systems are in
> statistical equilibrium and therefore share temperature parameters
> are well studied in statistical physics, but I haven't followed
> this up.
>

Tell me if I understand this correctly: it looks like each commodity type has a
different temperature, ML.  In that case each commodity is a macrosystem, or
macrosubsyatem, and these subsyatems are therefore not in thermal equilibrium.
Cf Duncan Foley's paper where agemts are macrosystems.

Could M be the common temperature? And k/L the price variate.
```

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