Alpha-invariant of Toric Line Bundles

We generalize the work of Jian Song to compute the alpha invariant of any (nef and big) toric line bundle in terms of the associated polytope. We use the analytic version of the computation of the log canonical threshold of monomial ideals to give the log canonical threshold of any non-negatively curved singular hermitian metric on the line bundle, and deduce the alpha invariant from this.Comment: 13 pages. Minor corrections, and references added. Published versio

The effect of local political deliberation on the publicity of reason

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The second law of thermodynamics at the microscopic scale

In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this paper, we investigate how the relaxation toward equilibrium is made possible through interactions that do not lead to significant exchange of energy, and argue for the validity of the second law of thermodynamics at the microscopic scale.Comment: 3 pages, 1 figur