The second law of thermodynamics states that entropy, as a measure of randomness in a system, increases over time. Although studies have investigated biological sequence randomness from different aspects, it remains unknown whether sequence randomness changes over time and whether this change consists with the second law of thermodynamics. To capture the dynamics of randomness in molecular sequence evolution, here we detect sequence randomness based on a collection of eight statistical random tests and investigate the randomness variation of coding sequences with an application to Escherichia coli. Given that core/essential genes are more ancient than specific/non-essential genes, our results clearly show that core/essential genes are more random than specific/non-essential genes and accordingly indicate that sequence randomness indeed increases over time, consistent well with the second law of thermodynamics. We further find that an increase in sequence randomness leads to increasing randomness of GC content and longer sequence length. Taken together, our study presents an important finding, for the first time, that sequence randomness increases over time, which may provide profound insights for unveiling the underlying mechanisms of molecular sequence evolution.
