{"paper":{"title":"Minimum Power to Maintain a Nonequilibrium Distribution of a Markov Chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","physics.bio-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dmitri S. Pavlichin, Tsachy Weissman, Yihui Quek","submitted_at":"2019-07-02T18:39:38Z","abstract_excerpt":"Biological systems use energy to maintain non-equilibrium distributions for long times, e.g. of chemical concentrations or protein conformations. What are the fundamental limits of the power used to \"hold\" a stochastic system in a desired distribution over states? We study the setting of an uncontrolled Markov chain $Q$ altered into a controlled chain $P$ having a desired stationary distribution. Thermodynamics considerations lead to an appropriately defined Kullback-Leibler (KL) divergence rate $D(P||Q)$ as the cost of control, a setting introduced by Todorov, corresponding to a Markov decisi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01582","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}