Aquino Gerardo, Bologna Mauro, West Bruce J, Grigolini Paolo
Faculty of Natural Sciences, Imperial College London, London, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051130. doi: 10.1103/PhysRevE.83.051130. Epub 2011 May 31.
We study the transport of information between two complex systems with similar properties. Both systems generate non-Poisson renewal fluctuations with a power-law spectrum 1/f(3-μ), the case μ=2 corresponding to ideal 1/f noise. We denote by μ(S) and μ(P) the power-law indexes of the system of interest S and the perturbing system P, respectively. By adopting a generalized fluctuation-dissipation theorem (FDT) we show that the ideal condition of 1/f noise for both systems corresponds to maximal information transport. We prove that to make the system S respond when μ(S)<2 we have to set the condition μ(P)<2. In the latter case, if μ(P)<μ(S), the system S inherits the relaxation properties of the perturbing system. In the case where μ(P)>2, no response and no information transmission occurs in the long-time limit. We consider two possible generalizations of the fluctuation dissipation theorem and show that both lead to maximal information transport in the condition of 1/f noise.
我们研究了两个具有相似性质的复杂系统之间的信息传输。两个系统都产生具有幂律谱1/f(3 - μ)的非泊松更新涨落，μ = 2的情况对应于理想的1/f噪声。我们分别用μ(S)和μ(P)表示感兴趣的系统S和扰动系统P的幂律指数。通过采用广义涨落耗散定理（FDT），我们表明两个系统的1/f噪声的理想条件对应于最大信息传输。我们证明，当μ(S) < 2时，为使系统S做出响应，我们必须设定条件μ(P) < 2。在后一种情况下，如果μ(P) < μ(S)，系统S继承扰动系统的弛豫特性。在μ(P) > 2的情况下，在长时间极限下不会发生响应和信息传输。我们考虑了涨落耗散定理的两种可能推广，并表明两者都导致在1/f噪声条件下的最大信息传输。
