{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T21:43:45Z","timestamp":1778103825982,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T00:00:00Z","timestamp":1745539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This work explores the implications of assuming time symmetry and applying bridge-type, time-symmetric temporal boundary conditions to deterministic laws of nature with random components. The analysis, drawing on the works of Kolmogorov and Anderson, leads to two forms of governing equations, referred to here as symmetric and antisymmetric. These equations account for the emergence of characteristics associated with conventional thermodynamics, the arrow of time, and a form of antecedent causality. The directional properties of time arise from the mathematical structure of Markov bridges in proximity of the corresponding temporal boundary conditions, without requiring any postulates that impose a preferred direction of time.<\/jats:p>","DOI":"10.3390\/e27050466","type":"journal-article","created":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T08:02:57Z","timestamp":1745568177000},"page":"466","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Two Types of Temporal Symmetry in the Laws of Nature"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3148-471X","authenticated-orcid":false,"given":"A. Y.","family":"Klimenko","sequence":"first","affiliation":[{"name":"Centre for Multiscale Energy Systems, School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, Brisbane 4072, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hume, D. (1748). An Enquiry Concerning Human Understanding, Open Court Pub. Co.","DOI":"10.1093\/oseo\/instance.00032980"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Russell, B. (2009). Our Knowledge of the External World, Taylor and Francis.","DOI":"10.4324\/9780203875360"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Reichenbach, H. (1956). The Direction of Time, University of California Press.","DOI":"10.1063\/1.3059791"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zalta, E.N., and Nodelman, U. (2001). Causation and Manipulability. 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