The polythermal ensemble: A rigorous interpretation of temperature fluctuations in statistical mechanics Available to Purchase

The usual treatment of temperature fluctuations in thermometry is based on an analysis of fluctuations in a mechanical variable in a system of constant temperature. This calculation is here inverted to discuss the uncertainty in the temperature for a system whose mechanical variables have been measured. The inversion is accomplished by introducing a new statistical‐mechanical ensemble, the polythermal ensemble, which is obtained as an extension of the canonical ensemble. It is shown that temperature fluctuations in very small systems are larger than is sometimes believed. This is a sense in which β=(k_BT)⁻¹ is a more fundamental variable than is the temperature T.