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Many recent models of trade dynamics use the simple idea of wealth exchangesamong economic agents in order to obtain a stable or equilibrium distributionof wealth among the agents. In particular, a plain analogy compares the wealthin a society with the energy in a physical system, and the trade between agentsto the energy exchange between molecules during collisions. In physicalsystems, the energy exchange among molecules leads to a state of equipartitionof the energy and to an equilibrium situation where the entropy is a maximum.On the other hand, in the majority of exchange models, the system converges toa very unequal condensed state, where one or a few agents concentrate all thewealth of the society while the wide majority of agents shares zero or almostzero fraction of the wealth. So, in those economic systems a minimum entropystate is attained. We propose here an analytical model where we investigate theeffects of a particular class of economic exchanges that minimize the entropy.By solving the model we discuss the conditions that can drive the system to astate of minimum entropy, as well as the mechanisms to recover a kind ofequipartition of wealth.

Entropy and equilibrium state of free market models