About thermometers and temperature

Abstract

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.

19 pages, 8 figures

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Cited by in corpus (12)

• Statistical Mechanics of Systems with Negative Temperature
• Statistical mechanics of systems with long-range interactions and negative absolute temperature
• Langevin equation in systems with also negative temperatures
• The Role of Data in Model Building and Prediction: A Survey Through Examples
• How to define temperature in active systems?
• Microcanonical entropy for classical systems
• Temperature as a quantum observable
• Modeling the Efficiency and Effective Temperature of Bacterial Heat Engines
• Brownian Thermometry Beyond Equilibrium
• Negative-temperature Fourier transport in one-dimensional systems
• H-theorem at negative temperature: the random exchange model with bounds
• Effective Equations in complex systems: from Langevin to machine learning