Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

Investigation on the homogeneity and stability of aqueous nano cellulose suspensions prepared using pluronic F-127

This paper presents the results of experimental investigation on the aqueous dispersion behaviour of micro crystalline cellulose (MCC) prepared using Pluronic F-127. For this purpose, different concentrations (0.5-3.0 wt.%) of MCC were dispersed in water with the help of ultrasonication technique using various concentrations of Pluronic F-127. The homogeneity of the suspensions and agglomerations were characterized by optical and transmission electron microscopy and the concentration of well dispersed MCC was measured using UV-Vis spectroscopy. Also, the suspensions were subjected to high speed ultracentrifugation at 3000 rpm and observed visually for sedimentation and subsequently, concentration was calculated using UV-Vis, in order to assess the long term stability of the suspensions. Based on these experiments, optimum concentration of Pluronic to disperse different MCC concentrations has been suggested.