Eukaryote genomes contain excessively introns, intergenic and other non-genic sequences that appear to have no vital functional role or phenotype manifestation. Their existence, a long-standing puzzle, is viewed from the principle of increasing entropy. According to thermodynamics of open systems, genomes evolve toward diversity by various mechanisms that increase, decrease and distribute genomic material in response to thermodynamic driving forces. Evolution results in an excessive genome, a high-entropy ecosystem of its own, where copious non-coding segments associate with low-level functions and conserved sequences code coordinated activities. The rate of entropy increase, equivalent to the rate of free energy decrease, is identified with the universal fitness criterion of natural selection that governs populations of genomic entities as well as other species.