By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） el...By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.展开更多
This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of t...This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10874174)the Research Foundation of the Education Department of Jiangxi Province of China (Grant No.GJJ10097)
文摘By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.
文摘This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos.
