Continuing with Beinhocker’s Origin of Wealth, it is important to distinguish carefully between some of the ideas that Beinhocker is expounding. While overall, he is doing a good job of bringing in many related thoughts and ideas, there is a slight tendency towards “mushing.”

In that note, I’d like to suggest that we discern carefully between ideas involving utility (Origins, hardcover; pp. 34 & 37), and equilibrium. On pg. 34, Beinhocker begins a discussion of how utility is an underlying concept that allows us to model system dynamics, in which two or more parties are each separately trying to optimize their own position. On pg. 37, he introduces the notation of a util, which has further been subsumed into other measures and approaches.

We need to go back to what we learned in our first semester of chemistry: unit analysis.

The fundamental units of a free energy equation (Helmholtz or Gibbs) are energy. The enthalpy is an energy term, and while entropy is label-less, temperature is an energy term.

We define the equilibrium point as when the derivative of the free energy reaches zero. Thus, equilibrium is when we at the lowest possible point in the energy content of the system. And we need — whenever we make analogy of equilibrium to some other process or system — to first ensure that we are modeling something that can be described as at least an analogy to energy.

In contrast, utility is something that active, dynamic agents seek to optimize. They are not seeking to minimize, but rather maximize utility.

Equilibrium systems must intrinsically be characterized by those with a statistically large enough number of units so that the idea of distributing units among all available “energy states” (entropy) makes sense. And in simplest possible terms, there have to be at least two different energy states that these units could occupy, otherwise the idea of “distribution” doesn’t make sense.

Conversely, one can compute utility functions for systems with very small numbers of units. In such systems, the 2nd law of thermodynamics does not necessarily apply; we are trusting that the individual units have the wherewithal to optimize their respective utilities.

Utility functions are of great advantage in control and optimization theory. They are an excellent, in fact a necessary, component for both predictive analysis systems.

One of the best ways to understand refinements to the role of utility is to examine it in the context of neurocontrol, see e.g. Paul Werbos’s chapter on A Menu for Designs of Reinforcement Learning Over Time, in Neural Networks for Control, edited by Miller, Sutton, and Werbos [1990].

But we need to make a clear distinction between systems which can be characterized by equilibrium processes, and those characterized by utility optimization.

I suggest that the reader slow down, read carefully, and use his or her own powers of discernment to cut through this Gordian knot of multiple intertwining concepts. They are all useful, and all powerful, but need to be carefully disambiguated.