Understanding the evolution of communities in developer social networks (DSNs) around open source software (OSS) projects can provide valuable insights about the socio-technical process of OSS development. Existing studies show the evolutionary behaviors of social communities can effectively be described using patterns including split, shrink, merge, expand, emerge, and extinct. However, existing pattern-based approaches are limited in supporting quantitative analysis, and are potentially problematic for using the patterns in a mutually exclusive manner when describing community evolution. In this work, we propose that different patterns can occur simultaneously between every pair of communities during the evolution, just in different degrees. Four entropy-based indices are devised to measure the degree of community split, shrink, merge, and expand, respectively, which can provide a comprehensive and quantitative measure of community evolution in DSNs. The indices have properties desirable to quantify community evolution including monotonicity, and bounded maximum and minimum values that correspond to meaningful cases. They can also be combined to describe more patterns such as community emerge and extinct. We conduct studies with real-world OSS projects to evaluate the validity of the proposed indices. The results suggest the proposed indices can effectively capture community evolution, and are consistent with existing approaches in detecting evolution patterns in DSNs with an accuracy of 94.1%. The results also show that the indices are useful in predicting OSS team productivity with an accuracy of 0.718. In summary, the proposed approach is among the first to quantify the degree of community evolution with respect to different patterns, which is promising in supporting future research and applications about DSNs and OSS development.