Statistical mechanics and thermodynamics of texts from various authors in the English language

Just as pairwise energetic interactions (e.g., Lennard-Jones) can inform model Hamiltonians from which the statistical mechanics and thermodynamics of physical systems can be studied, it is possible to study analogous quantities in the English language by considering the specific sequences of letters in words to be the result of ``energetic’’ interactions between pairs of these letters. Previous work has used the empirical frequencies of letters in words, in combination with Jaynes’ principle of maximum entropy, to obtain the interaction potentials which maximize the entropy of the resulting Boltzmann distribution of the energy of words [1,2]. In this work, we obtain these interaction potentials for various authors and examine differences in the resulting ``thermodynamic’’ properties. We find that signals in the quantity analogous to the heat capacity indicate changes in an author’s word use (both type and composition) and, moreover, that this quantity can be used to distinguish between authors.

[1] G. J. Stephens and W. Bialek, Physical Review E 81, 066119 (2010)

[2] A. Corral and M. G. del Muro, Entropy 22, 179 (2020)