Economic entropy:
Suppose, a nation gathers all the resources its citizens have and then divides the total resources equally among all the citizens. Will this nation progress? It would fail badly due to the economic entropy. The economic entropy means that the same resources are there, but they cannot be employed to benefit the people and the nation. Megastructures like factories and companies cannot be established. No new resources could be generated.
I don't know if this is related to your question, but maybe it can help. Some time ago, I fell into the trap of thinking that high entropy was related to increased public participation in society. As in your example, if we divide the physical capital of a city among its inhabitants, we will increase entropy (it will be more challenging to manage firms, etc.). But this does not apply to all cases. For example, suppose we replace the decentralized pricing system (invisible hand) with a planned approach; in that case, we will increase disorder (entropy) in society and realize that the number of goods offered will drop. The same comparison is valid for democratic and authoritarian regimes (the last one is more concentrated but with greater entropy). Even in the case of your example: if we imagine that the division of capital is done by the division of shares (and not the physical capital itself), the distribution of wealth in society will increase, and, probably, there will be a reduction in the disorder (inequality, poverty, etc).
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