symmetry ηc(f,r)=ηc(1−f,r) where r is the ratio of the volumes of the objects. Knowledge of this symmetry has the following …

role of symmetry. It is shown how certain symmetries can obstruct period doubling and Hopf bifurcations; the associated … routes to chaos cannot proceed until these symmetries have been broken. The symmetry approach also reveals the general …

propose a new structure entropy based on automorphism partition. Analysis of extreme cases shows that entropy based on … summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are more heterogeneous in the … structural heterogeneity is strongly negatively correlated to symmetry of real networks. …

The linear response framework was established a half-century ago, but no persuasive direct derivation of entropy … of the entropy production in the present theory is given by (dS/dt)irr=(dU/dt)/T with the internal energy U(t) of the …, the correct entropy production is given by the second-order symmetric term ρ2(t) as (dS/dt)irr=(1/T)TrH0ρ2′(t). This is …

We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg XXZ spin chain. The XXZ …

relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric … filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in …

a glass. The statistical entropy decreases by kln(4) at the glass transition and tends to that of the crystal at the …