All living systems need to obtain energy, learn about their environments, and maintain their internal state. The complexity of these processes varies enormously across different types of life, from the simple chemotactic foraging of \textit{E. coli} to the complex behaviours of mammals. In spite of this complexity, there may be general statements we can make about the processes of learning and homeostasis that are valid across the range of complexity we see in nature and even beyond. This thesis contains a series of explorations on these themes, linked by the central importance of energetic considerations.

In Part I we outline a class of stochastic models for understanding homeostatic behaviour and alleviating modelling challenges presented by conventional ethological tools. We apply this model class to understand feeding behaviour in rodents. In doing so we find that anorectic agents have different behavioural profiles compared to natural satiation, and uncover how information from the gut is integrated into feeding strategies that differ between night and day. Finally, we perform \textit{in silico} experiments and find behavioural interventions of comparable effectiveness to current anorectic agents.

In Part II we use stochastic thermodynamics to investigate the energetic constraints on learning and using a model of the world. We define an analytically-tractable system in which mutual information and work can be interchanged, and investigate the dynamics, efficiency, and regimes of operation of this system. We discover a regime in which information can act as a catalyst, allowing for increased work extraction. Next we define and investigate a thermodynamic system that performs online supervised learning. We find that learning in this system is inherently nonequilibrium and investigate the energetics of supervised learning.