  Many recent models of trade dynamics use the simple idea of wealth exchanges
among economic agents in order to obtain a stable or equilibrium distribution
of wealth among the agents. In particular, a plain analogy compares the wealth
in a society with the energy in a physical system, and the trade between agents
to the energy exchange between molecules during collisions. In physical
systems, the energy exchange among molecules leads to a state of equipartition
of 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 to
a very unequal condensed state, where one or a few agents concentrate all the
wealth of the society while the wide majority of agents shares zero or almost
zero fraction of the wealth. So, in those economic systems a minimum entropy
state is attained. We propose here an analytical model where we investigate the
effects 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 a
state of minimum entropy, as well as the mechanisms to recover a kind of
equipartition of wealth.
