In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

Convergence of a second-order shock-capturing scheme for the system of isentropic gas dynamics with L°° initial data is established by analyzing the entropy dissipation measures. This scheme is modified from the classical MUSCL scheme to treat the vacuum problem in gas fluids and to capture local entropy near shock waves. Convergence of this scheme for the piston problem is also discussed.

Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the trajectory manifold, and the entropy of the globally linearized manifold. When the entropies are Tsallis entropies the complexity is characterized by the value...

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibr...

We show that the state with the highest known average two-particle von Neumann entanglement entropy proposed by Sudbery and one of the authors gives a local maximum of this entropy. We also show that this is not the case for an alternative highly entangled state proposed by Brown et al.

We discuss the entropy of nonequilibrium steady states. We analyze the so-called spontaneous production of entropy in certain reversible deterministic nonequilibrium system, and its link with the collapse of such systems towards an attractor that is of lower dimension than the dimension of phase space. This means that in the steady state limit, the Gibbs entropy diverges to negative infinity. W...

The RST Model is given boundary term and Z-field so that it is well-posed and local. The Euclidean method is described for general theory and used to calculate the RST intrinsic entropy. The evolution of this entropy for the shockwave solutions is found and obeys a second law. E-mail address: [email protected]