Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach
We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature <i>T</i>. Synchronization is achieved by transmitting photons from one clock to another; the ab...
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MDPI AG
2025-06-01
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| author | Edward Bormashenko Michael Nosonovsky |
| author_facet | Edward Bormashenko Michael Nosonovsky |
| author_sort | Edward Bormashenko |
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| description | We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature <i>T</i>. 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’s 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. |
| format | Article |
| id | doaj-art-2d4ec150b0cb4534995dbfc17137f308 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-2d4ec150b0cb4534995dbfc17137f3082025-08-20T03:36:14ZengMDPI AGEntropy1099-43002025-06-0127769710.3390/e27070697Landauer Principle and Einstein Synchronization of Clocks: Ramsey ApproachEdward Bormashenko0Michael Nosonovsky1Department of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, IsraelDepartment of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USAWe introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature <i>T</i>. 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’s 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.https://www.mdpi.com/1099-4300/27/7/697Landauer boundsynchronization of clocksEinstein synchronizationRamsey theorylattice of clockscomplete graph |
| spellingShingle | Edward Bormashenko Michael Nosonovsky Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach Entropy Landauer bound synchronization of clocks Einstein synchronization Ramsey theory lattice of clocks complete graph |
| title | Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach |
| title_full | Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach |
| title_fullStr | Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach |
| title_full_unstemmed | Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach |
| title_short | Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach |
| title_sort | landauer principle and einstein synchronization of clocks ramsey approach |
| topic | Landauer bound synchronization of clocks Einstein synchronization Ramsey theory lattice of clocks complete graph |
| url | https://www.mdpi.com/1099-4300/27/7/697 |
| work_keys_str_mv | AT edwardbormashenko landauerprincipleandeinsteinsynchronizationofclocksramseyapproach AT michaelnosonovsky landauerprincipleandeinsteinsynchronizationofclocksramseyapproach |