  In this article, we have given a systematic formulation of the new
generalized competing mechanism: the Glauber-type single-spin transition
mechanism, with probability p, simulates the contact of the system with the
heat bath, and the Kawasaki-type spin-pair redistribution mechanism, with
probability 1-p, simulates an external energy flux. These two mechanisms are
natural generalizations of Glauber's single-spin flipping mechanism and
Kawasaki's spin-pair exchange mechanism respectively. On the one hand, the new
mechanism is in principle applicable to arbitrary systems, while on the other
hand, our formulation is able to contain a mechanism that just directly
combines single-spin flipping and spin-pair exchange in their original form.
Compared with the conventional mechanism, the new mechanism does not assume the
simplified version and leads to greater influence of temperature. The fact,
order for lower temperature and disorder for higher temperature, will be
universally true. In order to exemplify this difference, we applied the
mechanism to 1D Ising model and obtained analytical results. We also applied
this mechanism to kinetic Gaussian model and found that, above the critical
point there will be only paramagnetic phase, while below the critical point,
the self-organization as a result of the energy flux will lead the system to an
interesting heterophase, instead of the initially guessed antiferromagnetic
phase. We studied this process in details.
