Lijingjing's post on thermo-economics

Hi, this is Jingjing. Forgot my ID and password so i'm doing anonymously. My Statistic Mechanics knowledge is still in the level of undergraduate so dont laugh on me if common sense mistakes happen.

" Can relations found in individual decision maker be linearly zoomed to explain the behavior of a complex system? What kind of interactions we should consider when individuals are put into a system?"

I think the answer is "no". Actually, this is the key issue that we can make the resemblance between economics and thermodynamics. Considering a real thermodynamics system consist of a huge amount of particles. We have enough powerful tools to discribe the individual behavior of each particle: Newtonian low, quantum mechanics, relativity. Howerver, if you want to descripbe the whole system by solving the coupled equations discribing each single particle, it just becomes a mission impossible. Even in case as simple as 3 bodies, it has been proved more than one hundred years ago that there exist no analytical solutions to it(by Poncare, I believe). If numerical simulation approach used, it's a common sense that there is no way to predict the behavior of it by solving the dynamic equations of each particle numerically because of the calculation precision problem. That's why we need another angle of view to discribe such a system--and then thermaldynamics, a "statistic" method, was born.

Back to the economics system. The ability of micro-economics is more or less like those basic functions describing single partics (Newtonian funtions, Schindinger functions, or Eistein functions), while milions and milions people make an ensemble whose behavior can not be discribed by combining their personal decisions together, which is out of the ability of any person or computer. From this point of view, at least for me personally, it is no strange that we can find a lot of similarity between an economic system and a thermodynamic system. BTW: I don't think the difference of Fuling's and Xinyhn's behavior will be a difficulty for discribing the economic system. They are just different particles. Imagine how different the electrons, the mu particles, and the quarks are, but they are all in the frame of quantumn mechanics.

However, there may be a fetal drawback in the attempt of discribing the economic system by thermodynamic method, that is, the "rational decision" assumption as a principle of any economics theories. Such assumption equal to the argument that at least we can have, before even we can "find", a full "determinant" functions to describe single person behavior. However, human can never be absolute, and always, rational. What's worse is such un-rationality not only plays a role of minor correction to the behavior of the whole system, but sometimes determines a lot of major phenomenas. What's more pessimistic, the un-rationality origines not only from the less of education and training, but also from thermodynamics itself. Imagine how un-euqilibrium a thermodynamic system it is the human body itself, and how could you predict the behavior of such an un-equilibrium system determinantly, which has been proved to be impossible. (It worth noting that, actually there are two meanings when talk about "uncertainty". One is in the context of quantumn mechanics when talking about the uncertainty of quantumn particles. You can never determine the coordinate of a particle precisely which is the nature of the world, but you can still describe the behavior of the particle determinantly, only in a way different than our classical experience. The other is in the background of describing a complex system. The behavior of the system it self is "determinant" thanks to the basic equations behand each single unit. However, we can never find out the original conditions precisely enough, nor can we do the calculation precisely enough, so that the behavior of the system is out side of our ability of prediction).

Nevertheless, I still believe doing economics research thermodynamiclly can give a lot of help for us to describe the system better. After all, we're still in the stage of trying to understand what's going on to our society yet, far away to the level of finding out the final push behind everything. In this sense, thermodynamics will shine a lot insights into economics. It is just surprising imaging that a (huge) group of human bodies, who themselves are un-equilibrium thermodynamic systems, behaves so likely to a low-level thermodynamic system. Thermodynamics is displaying itself in different levels.

Well, like it or not, I'm putting so much into an old topic that maybe no one will notice anymore, but actually I'm feeling this is the most interesting one I had here, :) Let we PhD students talk more about philosophy...