  Zipf's law is the most common statistical distribution displaying scaling
behavior. Cities, populations or firms are just examples of this seemingly
universal law. Although many different models have been proposed, no general
theoretical explanation has been shown to exist for its universality. Here we
show that Zipf's law is, in fact, an inevitable outcome of a very general class
of stochastic systems. Borrowing concepts from Algorithmic Information Theory,
our derivation is based on the properties of the symbolic sequence obtained
through successive observations over a system with an unbounded number of
possible states. Specifically, we assume that the complexity of the description
of the system provided by the sequence of observations is the one expected for
a system evolving to a stable state between order and disorder. This result is
obtained from a small set of mild, physically relevant assumptions. The general
nature of our derivation and its model-free basis would explain the ubiquity of
such a law in real systems.
