Information Measure for Size Distribution of Avalanches in the Bak-Sneppen Evolution Model

Information of avalanche size distribution is measured by calculating information entropy (IE) in the Bak-Sneppen evolution model. It is found that the IE increases as the model evolves. Specifically, we establish the relation between the IE and the self-organized threshold f_c. The variation of the IE near the critical point yields an exponent entropy index E = (τ - 1)/σ, where τ and σ represent the critical exponents for avalanche size distribution and avalanche size cutoff, respectively. A new quantity D_τ(g) (g = 1-(f_c-G)^{(τ - 1)/σ}, where G is the gap of the current state), defined as 1-I_τ(g)/I_τ(1), with I_τ(g) and I_τ(1) being the IE for the current state and the critical one respectively, is suggested that it represent the distance between the state with gap G and the critical one.