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Using mathematical statistical mechanics methods, this paper shows that decisions to heavily promote entrepreneurship beyond a certain threshold in a society would lead to an increase in the society’s Gini coefficient, and thus to more economic inequalities. More specifically, we show that, in a heterogeneous society made up of both entrepreneurs (Es) and ordinary agents (OAs), economic inequalities reach a minimum at an optimal ratio of ‘Es to OAs’. When dealing with a purely homogeneous society made up of entrepreneurs only or ordinary agents only, economic inequalities would decrease as trading activities intensify among the society’s agents. In particular, ideologies that consist in flattening the wealth/income of citizens (as it was recommended, for example, by communist regimes in the last century) to reduce economic inequalities through strict government interventions, may not lead to positive outcomes. We also show that introducing a little heterogeneity into a purely homogeneous society will help reduce economic inequalities in this society. Thus, a society that is composed of ordinary agents only will see its economic inequalities decrease if a number of entrepreneurs join this society. Vice-versa, a society of entrepreneurs only will have its inequalities reduced if some ordinary agents join this society and engage the pre-existing entrepreneurs in trading activities; one could think of southern San Francisco Bay Area, Silicon Valley, as a concrete example of such a situation. To encourage ordinary agents become entrepreneurs, governments could design and implement tax-incentive policies for their respective societies. While such tax-incentive policies would help increase the number of entrepreneurs in the targeted society, they would also have unintended consequences: the society’s middle class gets depleted at equilibrium, and the inequalities that result from implementing the aforementioned policies will be uniformly bigger than the ones that result from an equal tax redistribution policy. The paper concludes with a discussion section that raises a number of questions about socio-economic phenomena and explains how these phenomena can be accounted for using physics laws and principles. [ABSTRACT FROM AUTHOR]