Many evolutionary changes of the amino acid sequences in proteins are conservative: the replacement of one amino acid by another residue has a far greater chance of being accepted if the two residues have similar properties. It is difficult, however, to identify relevant physicochemical properties that capture this similarity. In this paper we introduce a criterion that determines similarity from an evolutionary point of view. Our criterion is based on the description of protein evolution by a Markov process and the corresponding matrix of instantaneous replacement rates. It is inspired by the conductance, a quantity that reflects the strength of mixing in a Markov process. Furthermore we introduce a method to divide the twenty amino acid residues into subsets that achieve good scores with our criterion. The criterion has the time invariance property that different time distances of the same amino acid replacement rate matrix lead to the same grouping; but different rate matrices lead to different groupings. Therefore it can be used as an automated method to compare matrices derived from consideration of different types of proteins, or from parts of proteins sharing different structural or functional features. We present the groupings resulting from two standard matrices used in sequence alignment and phylogenetic tree estimation.