The liquid superheat limit and critical radius of bubbles in homogeneous nucleateboiling are determined in the present paper by using density fluctuation theory of statistical theomodynamics.

Based on the statistical mechanice, professor Boltzmann established the mathematical theory of second Iaw of thermodynamics and fluctuation theory.

Quantization and quantum fluctuations in a damped time-dependent inductive coupled electric circuit;

Quantum fluctuation of a mesoscopic inductance-resistance coupled circuit with power source in squeezed vacuum state;

Antithetic property of quantum fluctuations in mesoscopic second order circuit;

Thequantum fluctuations of the charge and current of the circuit in coherent state werestudied, the results show that the quantum fluctuations in the two circuits arecorrelated with each other, and the results are analysed and discussed.

On the basis of the charge discreteness,the quantum fluctuations fo the charge,current and energy in the mesoscopic metal dual rings are calculated by the minimum shift operator.

On the basis of the charge quantization,the quantum fluctuations of the charge,the current and the energy in the dissipative mesoscopic circuit are calculated by the character of the minimum shift operator.