Volume-contracting systems are entropy-reducing

At the beginning of cybernetics, homeostasis was roughly described as an entropy-reducing mechanism: achieved through negative feedback loops, it actively counteracts disorder and uncertainty to maintain a system behavior. Although the concept of entropy played a central role in the early foundations of cybernetics (notably in the work of Norbert Wiener) it has largely faded from mainstream control theory, except in specialized areas such as stochastic and information-theoretic control. In recent decades, control theory has focused on contracting systems (along with other incremental concepts) marking a shift away from classical notions of stability. Contraction emphasizes convergence between trajectories rather than convergence to a specific equilibria. In this short note, it is demonstrated that volume-contracting dynamics induce a reduction of entropy in probability distributions. This simple result reconnects modern contraction-based control with the original entropy-based perspective of early cybernetics.