Pure state quantum statistical mechanics and black holes

TL;DR

This paper reformulates quantum statistical mechanics using pure states, demonstrating that typical pure states exhibit thermal behavior in subsystems and applying this to black holes to suggest external states are likely thermal.

Contribution

It introduces a pure state formulation of quantum statistical mechanics and applies it to black holes, offering a new interpretation of probabilities in quantum systems.

Findings

Pure states' quantum statistics closely match ensemble mechanics.

Subsystems of typical states are nearly thermal.

External states of matter inside and outside black holes are likely thermal.

Abstract

Chapter 3 of S. Lloyd's 1988 Ph.D. thesis, `Black Holes, Demons, and the Loss of Coherence: How complex systems get information and what they do with it,' supervisor Heinz Pagels. Reformulates statistical mechanics in terms of pure states and shows that (a) quantum statistics of typical pure states are very close to the mechanics of statistical mechanical ensembles; (b) if a system is in a typical state with energy E, then the reduced density matrix of a subsystem is very close to a thermal state. (A similar result was derived using Levy's lemma some years later by S. Popescu, A.J. Short, A.Winter, Nature Physics 2, 754-758 (2006).) Pure state quantum statistical mechanics is applied to black holesto show that for typical states of matter insideand outside a black hole, the external state is likely to be thermal. Proposes novel interpretation of probabilities in quantum statistical mechanics. Full thesis available at http://meche.mit.edu/documents/slloyd_thesis.pdf. This chapter was submitted for publication to Physical Review in 1988 but rejected by one sentence referee report: `There is no physics in this paper.' You be the judge.