Abstract: Every thermodynamic quantity in the thermal equilibrium state can never bear large fluctuation.Specially, a criterion is proposed for the existence of the thermal equilibrium state in order to obey the requirement that both energy and entropy fluctuations must be small. Examples show that the number of particles 10^23 may be not large enough to guarantee the thermal equilibrium state for some systems at low temperature.

Key words: system of less particles, low temperature, entropy, energy, fluctuation