{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:27:51Z","timestamp":1760059671479,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,29]],"date-time":"2025-06-29T00:00:00Z","timestamp":1751155200000},"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>We introduce a synchronization procedure for clocks based on the Einstein\u2013Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T. Synchronization is achieved by transmitting photons from one clock to another; the absorption of a photon by a clock reduces the uncertainty in its timekeeping. The minimum energy required for this reduction in uncertainty is determined by the Landauer bound. We distinguish between the time-bearing and non-time-bearing degrees of freedom of the clocks. A reduction in uncertainty under synchronization in the time-bearing degrees of freedom necessarily leads to heat dissipation in the non-time-bearing ones. The minimum energy dissipation in these non-time-bearing degrees of freedom is likewise given by the Landauer limit. The same is true for mechanical synchronization of clocks. We also consider lattices of clocks and analyze synchronization using a Ramsey graph approach. Notably, clocks operating at the same temperature may be synchronized using photons of different frequencies. Each clock is categorized as either synchronized or non-synchronized, resulting in a bi-colored complete graph of clocks. By Ramsey\u2019s theorem, such a graph inevitably contains a triad (or loop) of clocks that are either all synchronized or all non-synchronized. The extension of the Ramsey approach to infinite lattices of clocks is reported.<\/jats:p>","DOI":"10.3390\/e27070697","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T07:42:06Z","timestamp":1751355726000},"page":"697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-2486","authenticated-orcid":false,"given":"Edward","family":"Bormashenko","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0980-3670","authenticated-orcid":false,"given":"Michael","family":"Nosonovsky","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,29]]},"reference":[{"key":"ref_1","first-page":"224","article-title":"Material History and Imaginary Clocks: Poincar\u00e9, Einstein, and Galison on Simultaneity","volume":"6","year":"2004","journal-title":"Phys. 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