• Jose Arrieta

Inequality, Structure, and Temperature

Physics as a whole encompasses the most successful predictive theories known to man. The unexplained variance in physics in some cases is in the order of one over 10 000 000 000 whereas in economics the denominator is lower than 5. So, it makes sense to imagine that structures, i.e. firms should eventually collapse. At least if our firms "follow the laws of thermodynamics". Yet, as Yuval Noah Harris explains in his Magnus opus, the opposite is the case. The human story is one of expansion and control. We as of today live in a single unified society that covers all continents and landmasses in the world. Sure there have been wars but the push for structure is higher than the pull for increasing entropy and equality.

The puzzle of why firms exist has not evaded economics. In fact, there is a whole bunch of theories at the foundation of economics trying to explain why people work in firms. They are called "theories of the firm" and indeed they jointly provide one answer to this question - the only one for economists - i.e. people can under broad conditions get more money while in a firm than freelancing in the market. The reasons being that it would take forever to write the contracts if all people were freelancers, that it's easier to acquire expensive things in a firm than as an individual, and that in the end knowledge is like fudge, sticky but also spills over so firms, just as candy wrappers, help to minimize the mess. Even with these variegated solutions, the puzzle is unsolved.

To explain the puzzle of structure in the push for entropy, let's go back to physics. In thermodynamics, there is the concept of free energy. Free energy has a strong track record in physics, being, in fact, the "only" element of physics in Feynman's quantum electrodynamics, i.e., the theory with the crazy predictive power from before. In fact, the free energy principle can be applied to every aspect of the discussion I just put forth by the work of the über genius Karl Friston. However, I still do not grasp his theories, so let me introduce free energy more simply.

Free energy is the amount of work one can do with a system. A system in thermodynamics is a container with gas inside, which is bounded by another gas-filled container. Both gases tend to be at different temperatures and the raison d'etre of thermodynamics is to bring them to equilibrium.

Now for any system, we can calculate the free energy as a combination of the entropy of the system, temperature, and internal energy. Yes, I said energy in the LHS and RHS. And that is the main point here. Free energy is a kind of efficiency factor that weighs down how much work we can do with the amount of internal energy we have in the system and the missing information we have about it (i.e. entropy).

This is confusing. But the point is that at higher temperatures, the available free energy is lower than at lower temperatures. If we take internal energy as the energy available to build structures that counteract the entropy, then need we can see that temperature at the end controls when we would have equality or when we would have structures controlling a system.

It seems that just as the surface of the Earth, our society has become colder. Even as new individuals are added to our thermodynamic chamber the overall temperature somehow keeps going down. As society cools down the number of free energy increases and thus the pursuit for larger structures. I wonder why and I hope the answer is not just the typical thermodynamics answer of non-ergodicity.

PS: Inequality is bad. It leads to all sorts of problems and more importantly to the creation of caste systems within the society and their spurious and unredeemable thought processes. Yet, I do not want to live in a freelancer society. Freelancers have endemic burnout and insecurity. The answer to inequality needs to be more nuanced than high or low. Yet, this post is long enough.

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