Research of static electric balance The charge distribution on the surface of conductor is not uniform. From diffusion effect, the current exists. The diffusion can affect the charge distribution. And the temperature can affect diffusion, thus it can affect the charge distribution. So the charge distribution is different when the temperature is 30 degree comparing to that when it is 50 degree. The distribution of constant potential of charges is unique and cannot vary with temperature. So the theory of is meaningless. If there is only diffusion current , the charge distribution will be uniform. Actually it is not that way. There is some corresponding movement inside for sure. Previously we deduced that there is potential difference on charged conductor. The potential difference can drive the current (see the following figure) and diffusion current “balanced”. Such mechanism also exists in the PN knot of Semiconductor. there are two forms of current of field of force J=r*E+u*f*ρ It is the combination of two experimental laws. Then diffusion is considered. The Brown movement on charged conductor is(see figure 1) J=-D*dρ/dx+r*E+u*f*ρ Web of "figure 1" is "http://photo.163.com/openpic.php?user=zbl1905&pid=147836835&_dir=%2F1386442" Figure 1 Thermodynamic figure of static electric balance Usually D,ρ,dρ/dx is small and r is big, so E and f are small. The theory of constant potential has only engineering meaning, which is approximate. The electric lines of force and electric field exist not only on the surface of a conductor. The electric lines of force can penetrate inside of the conductor. Inside the conductor, ρ tends to be 0. So J=r*E Conducting current will produce heat. Thus the inside temperature of the conductor will be a little higher than the surface. If it is just a cup of water on a table, we see stable balance. For charged conductor, figure 1 shows much heat transmission which can be observed. It is reasonable with the precedent theoretical background. Einstein introduced two kinds of thermal activities when he studied Brown movement in a field of force. J=-D*dρ/dx+u*f*ρ Considering Eistein Equation, we get J=-u（kT *dρ/dx+f*ρ） When J=0,the system is balanced, we get ρ=A*exp(-Ep/kT) For charged conductors, there are transmission factors D, u, and r. If there is only Einstein equation, the transmission factors cannot be extracted. The barely got balanced distribution will contain transmission factors of thermodynamics for sure(macro and micro thermodynamic transmission is not avoidable). And canonical distribution ρ=A*exp(-E/kT) only has direction relation with energy. From thermodynamic transmission, charged conductor does not support statistical mechanics with canonical distribution.