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From a chemical kinetics perspective, Kramers\u2019 theory provides a mapping from continuous dynamics to discrete-state chemical kinetics. Motivated by recent developments, this Perspective provides a rigorous way of performing such a mapping, explaining why and how Kramers\u2019 theory works from several points of view. In particular, we consider transitions of a Brownian particle between two potential wells corresponding to the \u201creactant\u201d and the \u201cproduct\u201d of a chemical reaction. A central unifying idea is to divide the equilibrium ensemble of possible states of the system into two sub-ensembles corresponding to the reactant and product states and then to consider fluxes between these sub-ensembles. Importantly, na\u00efve separation based on the location measured relative to the barrier top does not result in a mapping that is physically tenable, and instead, the past of the trajectory should be considered. Thus, constructed reactant and product ensembles provide an internally consistent description of the problem when also viewed from two different perspectives: one based on the definition of the rate as a conditional transition probability per unit time and the other based on the relaxation modes of the time-evolution operator governing the dynamics.<\/jats:p>","DOI":"10.1063\/5.0352910","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T10:39:18Z","timestamp":1790678358000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Activated rate processes viewed through unidirectional fluxes at equilibrium, correlation functions, and splitting probabilities"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0564-0408","authenticated-orcid":false,"given":"Alexander M.","family":"Berezhkovskii","sequence":"first","affiliation":[{"name":"1 Retired, Bethesda, Maryland 20814, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4023-187X","authenticated-orcid":false,"given":"Kevin","family":"Song","sequence":"additional","affiliation":[{"name":"Oden Institute for Computational Engineering and Sciences, University of Texas at Austin 2 , Austin, Texas 78712,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8421-1846","authenticated-orcid":false,"given":"Dmitrii E.","family":"Makarov","sequence":"additional","affiliation":[{"name":"Oden Institute for Computational Engineering and Sciences, University of Texas at Austin 2 , Austin, Texas 78712,","place":["USA"]},{"name":"Department of Chemistry, University of Texas at Austin 3 , Austin, Texas 78712,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"2026092906390207000_c1","volume-title":"Free Energy Transduction and Biochemical Cycle Kinetics","year":"1989"},{"key":"2026092906390207000_c2","volume-title":"Physical Biology of the Cell","year":"2013","edition":"2"},{"key":"2026092906390207000_c3","volume-title":"Motor Proteins and Molecular Motors","year":"2015"},{"key":"2026092906390207000_c4","volume-title":"Single Molecule Science: Physical Principles and Models","year":"2015"},{"key":"2026092906390207000_c5","volume-title":"Stochastic Thermodynamics","year":"2025"},{"key":"2026092906390207000_c6","volume-title":"Stochastic Thermodynamics","year":"2021"},{"key":"2026092906390207000_c7","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s10704-010-9535-0","article-title":"The resistance curve for subcritical cracks near the threshold","volume":"167","year":"2011","journal-title":"Int. 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