I thought I'd show how causal entropic forces can reproduce a demand curve. The background is here. I set up a simple system where there is a budget constraint such that
Q₁ p₁ + Q₂ p₂ ≤ 10
starting with p₁ = p₂ = 1. I compute a few time steps, letting the system reach equilibrium. After that, I steadily increase the price p₁ by 0.1 for 10 time steps (until it reaches p₁ = 2). As we can see in the graphs below, this traces out a demand curve. I also show the budget constraint region as well as the time series of quantity demanded. The theoretical solution is shown as a gray dotted line.