Isobaric yield ratio difference and Shannon information entropy

The Shannon information entropy theory is used to explain the recently proposed isobaric yield ratio difference (IBD) probe which aims to determine the nuclear symmetry energy. Theoretically, the difference between the Shannon uncertainties carried by isobars in two different reactions (ΔIn21ΔIn21), is found to be equivalent to the difference between the chemical potentials of protons and neutrons of the reactions [the IBD probe, IB-Δ(βμ)21Δ(βμ)21, with β   the reverse temperature]. From the viewpoints of Shannon information entropy, the physical meaning of the above chemical potential difference is interpreted by ΔIn21ΔIn21 as denoting the nuclear symmetry energy or density difference between neutrons and protons in reactions more concisely than from the statistical ablation–abrasion model.