I think recent history shows that particular individuals are not just statistics. What about influential politicians and businessmen? I am thinking of people like Donald Trump and Jeff Bezos. Also, please note what Karl Popper said about theories of history, which he called “historicism”. A great deal of history is influenced by powerful people doing what they feel like, which is not always rational.

]]>It seem that exist a Lagrangian in a critical point

the Euler-Lagrange equation is

that has two solution

or

then if there is this econophysics Lagrangian, then there are critical index, and surely phases. I write this result in vixra, where I write immediately results that look beautiful.

I am thinking that the temporal dynamics of an economic system could be modeled by:

and

when the system is in equilibrium

so that the economic system has an equilibrium point, phase transition and critical exponent, if there are interaction between individual agents. These equilibrium point are solution of the dynamics, when the system does not oscillate due to dispersion, or when the initial condition is (a constant economic potential).

When the extensive quantity are near a critical point, then the equilibrium points change a lot with small perturbations, and so the trajectories change a lot with small perturbations: the economic system is unstable in the temporal evolution, and the economic system is near a critical point.

I am learning the Landau theory of phase transition, that has an approximation of the thermodynamics potential in a Taylor series near a critical point (instead of an approximation of a differential equation, that could give a dynamics).

A possible differential equation for a critical point is but it is not a differential equation obtained from a Lagrangian, so that an analogy with physical system with potential and kinetic energy is not possible.

Perhaps it might be possible to model thermodynamic systems that vary over time: thermodynamic oscillations or irreversible transformations.

I didn’t quote Fisher’s thesis. I’ve tried to make that clearer.

]]>Thanks! By the way, about this:

For example, any monotonically increasing transformation of the utility function preserves the rank-ordering. If you wanted to make an analogy to physics, you might consider such monotonic transformations a “gauge freedom.” The reason you can’t add utilities of different individuals is because what you get is physically meaningless, not merely unimportant (it reminds me of Feynman complaining about a textbook which asked students to work out the “total temperature” of two stars). What would it mean to add two rank orderings?

I was trying to allude to this “gauge freedom” when I wrote:

Furthermore, if we believe we can reparametrize the utility of each agent without changing anything, it makes no sense to add utilities.

Of course I was keeping a more agnostic attitude when I wrote “if we believe”. I just didn’t want to commit to using “utility” in the way many economists do, where it’s purely a way of referring to a preference relation. I wasn’t wanting to argue *against* using the word this way, either.

Please let me know if you come out with a paper on thermodynamics and economics.

]]>That said, there is one economically meaningful way to add up people’s desires: you add up people’s willingness to pay. The maximum you are willing to pay for X is the value of X to you, and this is a property of your preference relation. This is basically what economists talk about when they talk about consumer surplus, producer surplus etc. The disadvantage is it treats everyone’s dollars the same. You could construct a measure that gave greater weight, say, to a poor man’s dollars to a rich man’s, but economic theory necessarily tells you nothing about what the relative weight should be since from an economic standpoint all dollars are interchangeable — you have to step outside economics and make an arbitrary value judgement.

Finally, I will cryptically remark that I have my own ideas of how to apply thermodynamic ideas in economics very different from the conventional analogies but I will not say what they are because I want to write a paper about it!

]]>Maybe, but there’s a funny thing going on here. In classical mechanics we use symplectic (and contact) geometry to describe dynamics, but in classical thermodynamics we use them to describe statics: that is, equilibrium situations. The analogy to economics discussed in this paper by Smith and Foley mainly concerns statics!

In statics, Hamilton’s equations play a different role than we’re used to. In classical mechanics they’re called the ‘Maxwell relations’. I tried to explain this here:

• Classical mechanics versus thermodynamics (part 1).

• Classical mechanics versus thermodynamics (part 2).

I guess it can still make sense to study complete integrability in classical thermodynamics. But I don’t have much of a feeling for what it means! So that’s a good puzzle to add to my list. I’m thinking about this stuff again these days.

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