From Boltzmann to Zipf through Shannon and Jaynes The wordfrequency distribution provides the fundamental building blocks that generate discourse in natural language. It is well known, from empirical evidence, that the wordfrequency distribution of almost any text is described by Zipfxe2x80x99s law, at least approximately. Following Stephens and Bialek (2010), we interpret the frequency of any word as arising from the interaction potentials between its constituent letters. Indeed, Jaynesxe2x80x99 maximumentropy principle, with the constrains given by every empirical twoletter marginal distribution, leads to a Boltzmann distribution for word probabilities, with an energylike function given by the sum of the alltoall pairwise (twoletter) potentials. The socalled improved iterativescaling algorithm allows us finding the potentials from the empirical twoletter marginals. We considerably extend Stephens and Bialekxe2x80x99s results, applying this formalism to words with length of up to six letters from the English subset of the recently created Standardized Project Gutenberg Corpus. We find that the model is able to reproduce Zipfxe2x80x99s law, but with some limitations: the general Zipfxe2x80x99s powerlaw regime is obtained, but the probability of individual words shows considerable scattering. In this way, a pure statisticalphysics framework is used to describe the probabilities of words. As a byproduct, we find that both the empirical twoletter marginal distributions and the interactionpotential distributions follow welldefined statistical laws.

How the Probabilistic Structure of Grammatical Context Shapes Speech Does systematic covariation in the usage patterns of forms shape the sublexical variance observed in conversational speech? We address this question in terms of a recently proposed discriminative theory of human communication that argues that the distribution of events in communicative contexts should maintain mutual predictability between language users, present evidence that the distributions of words in the empirical contexts in which they are learned and used are geometric, and thus support this. Here, we extend this analysis to a corpus of conversational English, showing that the distribution of grammatical regularities and the subdistributions of tokens discriminated by them are also geometric. Further analyses reveal a range of structural differences in the distribution of types in parts of speech categories that further support the suggestion that linguistic distributions (and codes) are subcategorized by context at multiple levels of abstraction. Finally, a series of analyses of the variation in spoken language reveals that quantifiable differences in the structure of lexical subcategories appears in turn to systematically shape sublexical variation in speech signal.