Entropy and equilibrium state of free market models

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

Eosinophilic granulomatosis with polyangiitis: sequential use of mepolizumab following rituximab for inadequate asthma control despite vasculitis remission

We report the case of a 54-year-old woman with antineutrophilic cytoplasmic antibody-negative eosinophilic granulomatosis with polyangiitis presenting with mononeuritis multiplex, intestinal hemorrhage, cardiomyopathy, fever, and worsening asthma symptoms. She was initially treated with steroids and cyclophosphamide but eventually required rituximab to control a vasculitis flare. However, her asthmatic symptoms did not improve, despite attaining vasculitis remission. Symptoms abated only after the treatment transition to mepolizumab. After a 1-year interval, there were no further episodes of asthma exacerbation and no requirement for systemic steroid therapy. This report reinforces the use of rituximab for induction and maintenance of remission in patients with eosinophilic granulomatosis with polyangiitis and predominant vasculitic manifestations, whereas mepolizumab demonstrated better control of the persistent eosinophilic manifestations, ensuing sustained remission and improved quality of life