A Scaling Phenomenon in Shannon Information Uncertainty Difference of fragments in Heavy-ion Collisions

The Shannon information-entropy uncertainty (in brief as "information uncertainty") is used to analyze the fragments in the measured 140$A$ MeV $^{40, 48}$Ca + $^{9}$Be and $^{58, 64}$Ni + $^{9}$Be reactions. A scaling phenomenon is found in the information-uncertainty difference of fragments between the reactions. The scaling phenomenon is explained in a manner of canonical ensemble theory, and is reproduced in the simulated reactions by the antisymmetric molecular dynamics (AMD) and AMD + GEMINI models. The probes based on information uncertainty, requiring no equilibrium state of reaction, can be used in the non-equilibrium system, and bridge the results of the static thermodynamics models and the evolving dynamical transport models.