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The extent to which a temperature can be appropriately assigned to a smallquantum system, as an internal property but not as a property of any largeenvironment, is still an open problem. In this paper, a method is proposed forsolving this problem, by which a studied system is coupled to a two-levelsystem (probe) as a microscopic thermometer. For small quantum chaotic systems,we show that a temperature can be determined, the value of which is sensitiveto neither the form, location, and strength of the probe-system coupling, northe Hamiltonian and initial state of the probe. This temperature turns out tohave the form of Boltzmann temperature.

Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer