The Statistical Mechanics of Learning and Co-Adaptation in Heterogeneous Populations

Adaptation is a fundamental mechanism of growth. Scientists have developed statistical models in numerous contexts to characterize growth and its emergent behaviors, such as inequality, competition, and cooperation. However, we still lack a general adaptive mechanism that explains the emergence of growth in uncertain environments, preventing systematic exploration of the origins of agent heterogeneities. In this dissertation, I derive a theory of statistical growth among agents adapting to their environments. I then show several key results. First, that the average growth rate of agents' resources is governed by the information they hold about their environment. It follows that the learning process can attenuate growth rate disparities, reducing the long-term effects of heterogeneity on inequality. Second, I show how groups that optimally combine complementary information about resources maximize their effective growth rate. I show that these advantages are quantified by the information synergy embedded in the conditional probability of environmental states given agents' signals, such that groups with a greater diversity of signals maximize their collective information. Lastly, using simple, pairwise agent interactions, I show how agent preferences converge when driven by observation of each other's behaviors. These results demonstratew how the formal properties of information underlie the statistical dynamics of many complex processes across biological and social phenomena.