Thermodynamic Bayesian Inference
Framework that draws an analogy between thermodynamics and Bayesian probability theory to infer statistical models by treating inference as an energy-minimizing process.
In Thermodynamic Bayesian Inference, the principles of thermodynamics—such as energy, entropy, and free energy—are applied to Bayesian inference to better understand how probabilistic models converge to optimal solutions. By framing inference in terms of energy minimization, this approach can exploit tools from statistical mechanics to find the most probable model parameters given the data. Specifically, it connects Bayesian updating (refining a model based on new data) with the reduction of free energy in a system, emphasizing that model predictions improve as they "consume" uncertainty, much like physical systems seek states of lower energy. This analogy has led to deeper insights in fields such as machine learning, where thermodynamic quantities can be used to assess the efficiency and stability of learning algorithms.
The idea of uniting thermodynamics and Bayesian inference has roots in the late 20th century, when researchers began exploring parallels between physical systems and probabilistic models. However, the formal term "Thermodynamic Bayesian Inference" and its development gained more traction in the 2000s as interdisciplinary research between statistical mechanics, information theory, and machine learning advanced.
Some of the foundational work connecting thermodynamics and information theory comes from Edwin T. Jaynes, whose work in the 1950s laid the groundwork for using entropy and thermodynamic principles in statistical mechanics and inference. More recent contributions have come from researchers in Bayesian machine learning and statistical mechanics, including Karl Friston, who developed the free energy principle, widely used in neuroscience and AI to explain how systems minimize uncertainty.