I don’t really want to get to the mathematical derivation of Lyapunov functions but they are a class of equations that allow us to predict whether a process will reach a state of equilibrium.
One example of how a Lyapunov function be used in a real world situation is to model a Race to the Bottom situation.
Imagine a game where governments get to set the amount of investment taxation. The heuristic to set these taxes is to set it at 90% of the average of what other countries are setting last year so as to attract a larger share of investments from other countries. Over time, this game becomes a race to the bottom where the only equilibrium state is when every country imposes close to zero taxation.
This was probably what went around policy maker’s head when they tried turning our local stock exchange into a REIT hub. To attract other