Dokument: Inverse engineering of cooling protocols: From normal behavior to Mpemba effects
| Titel: | Inverse engineering of cooling protocols: From normal behavior to Mpemba effects | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=73927 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20260713-132414-1 | |||||||
| Kollektion: | Publikationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Texte » Artikel, Aufsatz | |||||||
| Medientyp: | Text | |||||||
| Autor: | Löwen, Hartmut [Autor] | |||||||
| Dateien: |
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| Stichwörter: | Mpemba effect , Newtonian cooling , Heating , Protocols , Anomalous cooling , Non-equilibrium | |||||||
| Beschreibung: | When a cup of hot coffee is suddenly put into a cold environment, it cools down as a function of time t until the internal temperature Tint of the coffee equals the external ambient temperature Text. This instantaneous shock-freezing corresponds to an imposed cooling protocol of the external temperature Text(t), ideally described as a step-function in time, causing the time-dependent change of the internal temperature Tint(t). While the effect of different given protocols Text(t) on the resulting system cooling behavior, embodied in Tint(t), has been studied extensively, we consider here the inverse question: for a given system cooling Tint(t) how can an appropriate protocol Text(t) be engineered to produce the desired prescribed Tint(t). We use both the phenomenological Newtonian equation for cooling and microscopic models, such as a discrete two-level system and a Brownian harmonic oscillator with time-dependent noise, to compute analytically the protocol Text(t) needed to achieve a prescribed Tint(t). We then discuss the same question for phenomenological generalizations of the Newtonian law which include anomalous Mpemba effects, overcooling, asymmetries in cooling and heating as well as delay phenomena. It is shown that backward-engineered protocols do not always exist and can be non-unique. The results are important for steering the cooling behavior by time-varying external heat sources in a systematic way. | |||||||
| Rechtliche Vermerke: | Originalveröffentlichung:
Löwen, H. (2026). Inverse engineering of cooling protocols: From normal behavior to Mpemba effects. Physica A, 698, Article 131763. https://doi.org/10.1016/j.physa.2026.131763 | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät | |||||||
| Dokument erstellt am: | 13.07.2026 | |||||||
| Dateien geändert am: | 13.07.2026 |
