Thermodynamical genetic algorithms (TDGA) simulate the competitive model between energy and entropy in annealing to harmonize the conflicts between selective pressure and population diversity in GA. But high computational cost restricts the applications of TDGA. In order to improve the computational efficiency, a measurement method of rating-based entropy (RE) is proposed. The RE method can measure the fitness dispersal with low computational cost. Then a component thermodynamical replacement (CTR) rule is introduced to reduce the complexity of the replacement, and it is proved that the CTR rule has the approximate steepest descent ability of the population free energy. Experimental results on 0-1 knapsack problems show that the RE method and the CTR rule not only maintain the excellent performance and stability of TDGA, but also remarkably improve the computational efficiency of TDGA.