Thermodynamics of physical observers

Abstract

Observers are not abstract entities but physical systems subject to physical laws and limitations. This dissertation investigates the thermodynamics of physical observers, focusing on how physical limits shape intelligent information processing and decision-making under uncertainty. Two model classes of generalized, partially observable information engines are introduced and analyzed. They extend Szilárd’s classic thought experiment to settings where the observer must infer relevant information from available data. Observers memorize information and use it to take actions. A simple physical model for making the memory is introduced and the thermodynamic costs of different encoding strategies are analyzed. Thermodynamically rational encodings maximize the net engine work output. They are probabilistic in general and outperform naive coarse graining based encodings. Through analytical and numerical studies, physical codebooks for rational decision-making are developed, characterizing thermodynamically optimal decision-making strategies in two classes of binary decision problems under uncertainty. A mapping is established between abstract binary decision problems and partially observable Szilárd engines. This makes the physical framework used here widely applicable, intimately linking decision theory and thermodynamics. Extending the analysis of classical physical observers to quantum observers requires a description in terms of quantum thermodynamics. This is not a straightforward extension, as important thermodynamic concepts such as work and heat are not uniquely defined in quantum thermodynamics. Two definitions of thermodynamic work are compared for qubit systems and it is shown that they only agree under specific conditions. Their comparison reveals a discrepancy in the work costs required for perfect preparation of qubit states, with possible implications for high fidelity information processing in quantum systems. The research presented in this dissertation opens the door to a principled approach to understanding information processing, learning, and decision-making in physical systems, both biological and artificial. By incorporating the observer into the thermodynamic analysis, it provides a novel perspective on the interplay between physics, information processing and decision making under uncertainty.