Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics.

In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.

Evidence for entropy maximisation in human free choice behaviour

The freedom to choose between options is strongly linked to notions of free will. Accordingly, several studies have shown that individuals demonstrate a preference for choice, or the availability of multiple options, over and above utilitarian value. Yet we lack a decision-making framework that integrates preference for choice with traditional utility maximisation in free choice behaviour. Here we test the predictions of an active inference model of decision-making in which an agent actively seeks states yielding entropy (availability of options) in addition to utility (economic reward). We designed a study in which participants freely navigated a virtual environment consisting of two consecutive choices leading to reward locations in separate rooms. Critically, the choice of one room always led to two final doors while, in the second room, only one door was permissible to choose. This design allowed us to separately determine the influence of utility and entropy on participants' choice behaviour and their self-evaluation of free will. We found that choice behaviour was better predicted by an inference-based model than by expected utility alone, and that both the availability of options and the value of the context positively influenced participants' perceived freedom of choice. Moreover, this consideration of options was apparent in the ongoing motion dynamics as individuals navigated the environment. These results show that free choice behaviour is well explained by an inference-based framework in which both utility and entropy are optimised.