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All living systems (up to and including societies and economies) are thermodynamically open, entropy reducing, flow networks. I am curious if there has been any attempt to understand economic systems in physical terms, or to form a physical basis for economic theory?

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Yes there are, the branch of economics doing this is called Econophysics.

However, it’s worth while noting that only some of the results of econophysics are accepted by profession. For example, gravity model of trade is widely accepted, but other ideas are not.

This is because you can go only so far by trying to understand living endogenous mechanisms using concepts from physics.

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