This paper found two special points in the space of the charge distribution resulting from thermal electron emission and summed up the characteristics of the two points. Some special characteristics exist between the two points, including constant direction of potential gradient, spontaneous process of remarkable deviation from equilibrium, inconsistence of the directions of forces and fluxes etc. This paper also analyzed the entropy production rates caused by the flow going with the potential gradient and the flow against the potential gradient, and found that the production rates caused by the two respective flows are non-zero and will not reach an extremum over time. It showed that the charge distribution is a kind of ordered structure which emerges spontaneously and exists without consuming energy. Analysis also showed that electron emission is a process that causes the system's entropy to decrease. This process is relatively independent; and breaking the oneness of relaxation mode can lead to the system's evolutionary bifurcation.