A study on the characteristics in a symmetry Boltzmann machine composed of two Boltzmann machines

We propose a symmetry Boltzmann machine as a model of the brain which has the left hemispherium cerebri and the right one. A symmetry Boltzmann machine is composed of two Boltzmann machines. In case of two independent Boltzmann machines, we consider irreversible processes in a symmetry Boltzmann machine. We are interested in the entropy which depends on time and focus on its time change. First, we try to understand Boltzmann machines from the viewpoint of thermodynamics. Next, we consider an average of energy as an extensive variable which describes the relatively long time or macroscopic states of the independent systems. Then we derive its affinity. The result says that the temperature of each system determines the macroscopic equilibrium. On the other hand, in case of two correlative Boltzmann machines, we simulate a simple learning by using our model. The results say that a single unit's power spectrum density looks like the white noise in the forward learning, but it becomes the 1f fluctuation in the reverse learning.