English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The theory of modular flow has proved extremely useful for applyingthermodynamic reasoning to out-of-equilibrium states in quantum field theory.However, the standard proofs of the fundamental theorems of modular flow usemachinery from Fourier analysis on Banach spaces, and as such are notespecially transparent to an audience of physicists. In this article, I presenta construction of modular flow that differs from existing treatments. The mainpedagogical contribution is that I start with thermal physics via the KMScondition, and derive the modular operator as the only operator that couldgenerate a thermal time-evolution map, rather than starting with the modularoperator as the fundamental object of the theory. The main technicalcontribution is a new proof of the fundamental theorem stating that modularflow is a symmetry. The new proof circumvents the delicate issues of Fourieranalysis that appear in previous treatments, but is still mathematicallyrigorous.

An intuitive construction of modular flow