What is the maximum rate at which entropy of a string can increase?

TL;DR

This paper models a falling string as a self-avoiding walk to analyze its entropy increase rate, demonstrating it reaches the maximum allowed by quantum theory, with implications for black hole entropy growth.

Contribution

It introduces a self-avoiding walk model for a falling string to quantify entropy spread and its maximum rate, linking string dynamics to quantum limits.

Findings

String entropy spreads at the maximum quantum rate.

The model aligns with Susskind's black hole horizon spreading.

Black hole entropy increase rate matches quantum maximum.

Abstract

According to Susskind, a string falling toward a black hole spreads exponentially over the stretched horizon due to repulsive interactions of the string bits. In this paper such a string is modeled as a self-avoiding walk and the string entropy is found. It is shown that the rate at which information/entropy contained in the string spreads is the maximum rate allowed by quantum theory. The maximum rate at which the black hole entropy can increase when a string falls into a black hole is also discussed.