Estimate of temperature and its uncertainty in small systems

Details Estimate of temperature and its uncertainty in small systems Estimate of temperature and its uncertainty in small systems

2011-06-23

arxiv.org/abs/1106.4848v1

Am. J. Phys 79, 777 (2011)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

The energy of a finite system thermally connected to a thermal reservoir may fluctuate, while the temperature is a constant representing a thermodynamic property of the reservoir. The finite system can also be used as a thermometer for the reservoir. From such a perspective the temperature has an uncertainty, which can be treated within the framework of estimation theory. We review the main results of this theory, and clarify some controversial issues regarding temperature fluctuations. We also offer a simple example of a thermometer with a small number of particles. We discuss the relevance of the total observation time, which must be much longer than the decorrelation time.

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