A large protein sequence database with over 31,000 sequences and 10 million residues has been analysed. The pair probabilities have been converted to entropies using Boltzmann’s law of statistical thermodynamics. A scoring weight corresponding to “mixing entropy” of the amino acid pairs has been developed from which the entropies of the protein sequences have been calculated. The entropy values of natural sequences are lower than their random counterparts of same length and similar amino acid composition. Based on the results it has been proposed that natural sequences are a special set of polypeptides with additional qualification of biological functionality that can be quantified using the entropy concept as worked out in this paper.