Zipf's law emerges asymptotically during phase transitions in communicative systems
This provides a theoretical explanation for a fundamental linguistic pattern, addressing a long-standing enigma in language evolution.
The study tackled the origin of Zipf's law in language by showing it emerges asymptotically from phase transitions in communicative systems, using Laplace transforms to demonstrate this scaling behavior explains natural language emergence.
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language communication systems emerge at an abrupt phase transition in the fidelity of mappings between symbols and objects. Since the phase transition approximates the Heaviside or step function, we show that Zipfian scaling emerges asymptotically at high rank based on the Laplace transform. We thereby demonstrate that Zipf's law gradually emerges from the moment of phase transition in communicative systems. We show that this power-law scaling behavior explains the emergence of natural languages at phase transitions. We find that the emergence of Zipf's law during language communication suggests that the use of rare words in a lexicon is critical for the construction of an effective communicative system at the phase transition.