Weighted relative entropy for phylogenetic tree based on 2-step Markov model. 
The degree of similarity of DNA sequences can be concluded according to the comparison of DNA sequences, which helps to speculate their relationship in respect of the structure, function and evolution.  In this paper, we introduce the fundamental of the weighted relative entropy based on 2-step Markov Model to compare DNA sequences.  The DNA sequence, consisted of four characters A, T, C, G, can be considered as a Markov chain.  By taking state space I={A, T, C, G} and describe the DNA sequences with 2-step transition probability matrix we can get the eigenvalue of the DNA sequence to define the similarity metric.  Therefore, we find a new method to compare the DNA sequences, which is used to classify chromosomes DNA sequences obtained from 30 species.  The phylogenetic tree built by the alignment-free method of the distance matrix resulted from the weighted relative entropy has clearer and more accurate division.