Action in Physics, Biology and AI

The application of physical concepts (Gibbs distribution, action functional and evolution operator) in various fields is discussed. It is shown that Koonin’s laws of genomic evolution (Gibbs distribution for an “interacting gene gas”) follow from the Feynman-Kac formula for a discrete Markov process. An analogy with the principle of least action in physics is discussed (the sum of “evolutionary efforts” along the path of genome generation is an analog of action). By analogy with this approach, the “Additive Compositionality” properties of the word2vec algorithm for embeddings of words in language models in AI are discussed as a manifestation of the Gibbs distribution for semantics of words.