A comprehensive guide covering the most critical machine learning equations, including probability, linear algebra, optimization, and advanced concepts, with Python implementations.
Entropy, once seen as a measure of disorder in physical systems, is now understood as a reflection of our ignorance and knowledge limitations. This evolving perspective links entropy to information theory and challenges traditional views of objectivity in science.
This article explains how hydrophobic effects aren't simply about 'attraction' but are primarily driven by entropy. Water's strong hydrogen bonding network is disrupted when nonpolar molecules are introduced, decreasing entropy. The system minimizes this by reducing the surface area of contact between water and the nonpolar substance, leading to aggregation – the hydrophobic effect. It also clarifies the role of enthalpy, which is often less significant than entropy in this process.
This article discusses using entropy and variance of entropy (VarEntropy) to detect hallucinations in LLM function calling, focusing on how structured outputs allow for identifying errors through statistical anomalies in token confidence.
Sorkin and colleagues have derived an equivalent of the second law of thermodynamics for living systems, which establishes a relation between such a cell’s active uptake of energy and its random-looking path in terms of entropy production.
This review article discusses the concept of entropy in statistical physics and its role as both a tool for inference and a measure of time irreversibility. It highlights the developments in stochastic thermodynamics and the principle of maximum caliber, emphasizing the importance of cross-talk among researchers in disparate fields.
Prompted by these conversations, a subset of us eventually wrote a paper on the foundations of equilibrium thermodynamics:
John Baez, Owen Lynch and Joe Moeller, Compositional thermostatics.
John Baez, Owen Lynch and Joe Moeller, Compositional thermostatics.
