This paper paves the way for a direct comparison of the process of megathrust earthquakes with cellular automaton (CA) and for modeling the catastrophic singularity of seismic events as a phase transition phenomenon. It is shown that the entropy production rate (EPR), which is a property of thermodynamically non-equilibrium systems, occasionally decreases sharply in the seismic process of the Great East Japan Earthquake (GEJE) of magnitude 9. The timing of the EPR decrease is found to be clearly different from that of earthquakes of magnitude less than 9, but close to the timing of the earthquake of magnitude 9. The decrease indicates a qualitative change from a time-dependent non-equilibrium system towards a static equilibrium system, which can be a phase transition. In the GEJE process, EPR is calculated from the binarized velocity deviation of ground vibrations found to be equivalent to velocity. The equivalence attributes to that the transformation between them does not change the α-tremor which is the curvature of the Fourier amplitude spectrum of the velocity, and that an arbitrary ground vibration can be defined by α-tremor. The α-tremor is a noise. However, it is associated with microearthquakes whose epicenter is close to the GEJE epicenter, and is an important component of the GEJE process. The binarization equivalence allows the ground vibration to be viewed as CA which consists of binary numbers.