Hemoglobin (Hb) is the O2-carrying protein in our blood. Unlike myoglobin, it has four sites allowing it to bind up to four O2 molecules. Additionally, the tendency of O2 to bind to each site increases as the other three sites become occupied (this is an example of a phenomenon known as positive cooperativity). To model this effect, consider a simplified hemoglobin-like protein with two binding sites. When no sites are occupied, the system energy is 0; when only one of the two sites is occupied, the energy is E; and when both sites are occupied, the energy is 2E J. Here J parameterizes the cooperativity, as when both sites are occupied, the energy is not simply the sum of the individual binding energies at each site.