Great collapse (kepler’s first law)

America's First Great Moderation

First Order Phase Transitions in Gravitational Collapse

In recent numerical simulations of spherically symmetric gravitational collapse a new type of critical behaviour, dominated by a sphaleron solution, has been found. In contrast to the previously studied models, in this case there is a finite gap in the spectrum of black-hole masses which is reminiscent of a first order phase transition. We briefly summarize the essential features of this phase ...

Quantum collapse and the second law of thermodynamics.

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum r...

Flowers of the First Law

Continuing our examination of “the flowers of the First Law” (http://www.mii.ucla.edu/causality/?p=1354), this posting looks at one of the most crucial questions in causal inference: “How generalizable are our randomized clinical trials?” Readers of this blog would be delighted to learn that one of our flowers provides an elegant and rather general answer to this question. I will describe this ...

The Great Alliance: History, Reason, and Will in Modern Law

Modern revolutions remind observers of social and political phenomena that power ultimately rests with political masses. The stability of legal and political orders over time indeed depends on a sufficient level of consent on the part of the governed. Absent support by the will of the governed, mechanisms that operate to obstruct destabilizing collective action on their part are destined to ult...