Thermodynamics as a theory of decision-making with information-processing costs

Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here, we propose a thermodynamically inspired formalization of bounded rational decision-making where information processing is modelled as state changes in thermodynamic systems that can be quantified by differences in free energy. By optimizing a free energy, bounded rational decision-makers trade off expected utility gains and information-processing costs measured by the relative entropy. As a result, the bounded rational decision-making problem can be rephrased in terms of well-known variational principles from statistical physics. In the limit when computational costs are ignored, the maximum expected utility principle is recovered. We discuss links to existing decision-making frameworks and applications to human decision-making experiments that are at odds with expected utility theory. Since most of the mathematical machinery can be borrowed from statistical physics, the main contribution is to reinterpret the formalism of thermodynamic free-energy differences in terms of bounded rational decision-making and to discuss its relationship to human decision-making experiments.