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We derive generalizations of TPT that remove the requirements of stationarity and of the ergodic limit and provide this powerful tool for the analysis of other dynamical scenarios: periodically forced dynamics and time-dependent finite-time systems. This is partially motivated by studying applications such as climate, ocean, and social dynamics. On simple model examples, we show how the new tools are able to deliver quantitative understanding about the statistical behavior of such systems. We also point out explicit cases where the more general dynamical regimes show different behaviors to their stationary counterparts, linking these tools directly to bifurcations in non-deterministic systems.\n<\/jats:p>","DOI":"10.1007\/s00332-020-09652-7","type":"journal-article","created":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T16:03:19Z","timestamp":1599753799000},"page":"3321-3366","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8188-8288","authenticated-orcid":false,"given":"Luzie","family":"Helfmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3897-5984","authenticated-orcid":false,"given":"Enric","family":"Ribera\u00a0Borrell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"Sch\u00fctte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8127-6804","authenticated-orcid":false,"given":"P\u00e9ter","family":"Koltai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,9,10]]},"reference":[{"key":"9652_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BFb0095237","volume-title":"Dynamical Systems","author":"L Arnold","year":"1995","unstructured":"Arnold, L.: Random dynamical systems. 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