Linear instability and statistical laws of physics
Linear instability and statistical laws of physics
We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, (i) the sensitivity to initial conditions is given by $ ξ=[1+(1-q)λ_q t]^{1/(1-q)}$ with $q=0$; (ii) the statistical entropy $S_q=(1-\sum_i p_i^q)/(q-1) …