About thermometers and temperature
| Autor: | Baldovin, M., Puglisi, A., Sarracino, A., Vulpiani, A. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2017) 113202 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/aa933e |
| Popis: | We discuss a class of mechanical models of thermometers and their minimal requirements to determine the temperature for systems out of the common scope of thermometry. In particular we consider: 1) anharmonic chains with long time of thermalization, such as the Fermi-Pasta-Ulam (FPU) model; 2) systems with long-range interactions where the equivalence of ensembles does not always hold; 3) systems featuring absolute negative temperatures. We show that for all the three classes of systems a mechanical thermometer model can be designed: a temporal average of a suitable mechanical observable of the thermometer is sufficient to get an estimate of the system's temperature. Several interesting lessons are learnt from our numerical study: 1) the long thermalization times in FPU-like systems do not affect the thermometer, which is not coupled to normal modes but to a group of microscopic degrees of freedom; 2) a thermometer coupled to a long-range system measures its microcanonical temperature, even at values of the total energy where its canonical temperature would be very different; 3) a thermometer to read absolute negative temperatures must have a bounded total energy (as the system), otherwise it heavily perturbs the system changing the sign of its temperature. Our study shows that in order to work in a correct way also in "non standard" cases, the proper model of thermometer must have a special functional form, e.g. the kinetic part cannot be quadratic. Comment: 19 pages, 8 figures |
| Databáze: | arXiv |
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