Information theory and irreversibility of the renormalization group flow Export

@article{citeulike:5951428, abstract = {We present an approach to the study of the renormalization group (RG) flow based entirely on the information theory. The average information loss under Wilsonian RG transformation is introduced as conditional entropy of the fast variables, which are integrated out, when the slow ones are held fixed. Its positivity leads to the decrease in total entropy under renormalization which is mainly due to the decrease in number of degrees of freedom. We also introduce a mutual information of fast and slow variables as a more adequate quantity to represent the changes in the system under renormalization. For certain decimation transformations positivity of mutual information directly leads to the monotonic growth of the entropy per lattice site along the RG flow. Several simple examples are considered and possible consequences of this observation are discussed.}, archivePrefix = {arXiv}, author = {Apenko, S. M.}, citeulike-article-id = {5951428}, citeulike-linkout-0 = {http://arxiv.org/abs/0910.2097}, citeulike-linkout-1 = {http://arxiv.org/pdf/0910.2097}, day = {12}, eprint = {0910.2097}, keywords = {information-theory, mutual-information, renormalization-group}, month = {Oct}, posted-at = {2009-11-09 01:01:39}, priority = {2}, title = {Information theory and irreversibility of the renormalization group flow}, url = {http://arxiv.org/abs/0910.2097}, year = {2009} }

TY - JOUR ID - citeulike:5951428 L3 - citeulike-article-id:5951428 N2 - We present an approach to the study of the renormalization group (RG) flow based entirely on the information theory. The average information loss under Wilsonian RG transformation is introduced as conditional entropy of the fast variables, which are integrated out, when the slow ones are held fixed. Its positivity leads to the decrease in total entropy under renormalization which is mainly due to the decrease in number of degrees of freedom. We also introduce a mutual information of fast and slow variables as a more adequate quantity to represent the changes in the system under renormalization. For certain decimation transformations positivity of mutual information directly leads to the monotonic growth of the entropy per lattice site along the RG flow. Several simple examples are considered and possible consequences of this observation are discussed. TI - Information theory and irreversibility of the renormalization group flow KW - information-theory KW - mutual-information KW - renormalization-group AU - Apenko, SM PY - 2009/Oct/12/ UR - http://arxiv.org/abs/0910.2097 ER -