  Zipf's law seems to be ubiquitous in human languages and appears to be a
universal property of complex communicating systems. Following the early
proposal made by Zipf concerning the presence of a tension between the efforts
of speaker and hearer in a communication system, we introduce evolution by
means of a variational approach to the problem based on Kullback's Minimum
Discrimination of Information Principle. Therefore, using a formalism fully
embedded in the framework of information theory, we demonstrate that Zipf's law
is the only expected outcome of an evolving, communicative system under a
rigorous definition of the communicative tension described by Zipf.
