Entropic time endowed in quantum correlations

TL;DR

This paper proposes a novel mechanism where quantum correlations serve as internal clocks, defining emergent time through entropic processes and information constraints, potentially leading to a holographic property of time in quantum systems.

Contribution

It introduces a microscopic model linking quantum correlations and entropic information measures to the emergence of time, incorporating a holographic aspect of conditional entropy.

Findings

Quantum correlations can define internal clocks for emergent time.

Time evolution can be realized through entropic processes driven by information constraints.

Conditional entropy about past events exhibits a holographic area law.

Abstract

A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily read out as internal, quantum clocks that define time via their relative phases. The model could realize emergent time evolutions which exhibit unitarity of quantum theory, while its underlying process is driven entropically. The key quantity turns out to be the amount of accessible information about the clocks recording past events. By postulating the so-called data-processing inequality (or strong subadditivity of entropy) as a fundamental, physical limitation about how information decays, we propose that conditional entropy about this past information should be constrained to be a positive constant. The proposal implies a holographic property of this conditional entropy in an analogous manner with the area law of entanglement entropy.