Energy and information of chaotic dynamical systems
It is postulated that a basic process operates on a minimal time-scale \(\Delta_0>0\) and its dynamics is governed over a space \(X\) by a nonlinear transformation \(\tau_{\Delta_0}\: X\to X\) which is manifested as a chaotic process \(\tau_\Delta =\tau_{\Delta_0}^N\) on a large observable time-scale \(\Delta=N\Delta_0\). It is assumed that \(\tau_\Delta\) possesses on observable measure \(\mu_\Delta\). Then the average energy \(E_\Delta\) and information \(I_\Delta\) is defined for the given dynamical system \((X,\tau_\Delta, \mu_\Delta)\). The conservation of energy is proved. It is also shown that \(E_\Delta = KI_\Delta^2\) for a constant \(K\). This allows the estimation of the information content of matter.
scientific article; zbMATH DE number 1884656
scientific article