Degradation stage detection and life prediction are important for battery health management and safe reuse. This study first proposes a method of detecting whether a battery has entered a rapid degradation stage without accessing historical operating data. In addition, to alleviate the burden of extensive training data, an effective method of selecting training data with high physical similarity to the test data is developed improving the model's overall performance. Six physics-informed features are extracted from an equivalent circuit model using the relaxation voltage. Unsupervised learning is employed to analyze the internal physics similarity of batteries. The relationship between features and degradation stages or battery life is described by the Gaussian process-based machine learning model. The proposed method is validated using 65 batteries of two types. The results demonstrate that the detection accuracy of the degradation stage exceeds 90 %, and the performance of the life prediction model achieves an improvement of up to 53.56 % in terms of the root mean square error compared to that of the benchmark. Both detection and prediction can be independent of historical data, showing promise in assessing whether a battery can be used in the second life and predicting battery life in real time.