We consider the temperature fluctuations of a small object. Classical
fluctuations of the temperature have been considered for a long time. Using the
Nyquist approach, we show that the temperature of an object fluctuates when in
a thermal contact with a reservoir. For large temperatures or large specific
heat of the object Cvβ, we recover standard results of classical
thermodynamic fluctuations =CvβkBβT2β. Upon
decreasing the size of the object, we argue, one necessarily reaches the
quantum regime that we call quantum temperature fluctuations. At temperatures
below TββΌβ/kBβΟ, where Ο is the thermal relaxation time
of the system, the fluctuations change the character and become quantum. For a
nano-scale metallic particle in a good thermal contact with a reservoir,
Tβ can be on a scale of a few Kelvin.Comment: 4 pages, 2 figure