Exotic Fluids Made of Open Strings

TL;DR

This paper analyzes the thermodynamics of open superstring gases at high energy, revealing effective two-dimensional behavior and Hagedorn corrections to the equation of state, with implications for string theory thermodynamics.

Contribution

It provides a detailed calculation of the entropy and equation of state for open superstrings, demonstrating high-energy two-dimensional behavior and stability near the Hagedorn temperature.

Findings

High energy entropy shows effective 2D behavior.

Hagedorn effects modify the Zeldovich equation of state.

Equilibrium states near Hagedorn temperature are stable.

Abstract

We compute the high energy entropy and the equation of state of a gas of open superstrings in the infinite volume limit focusing on the calculation of the number of strings as a function of energy and volume. We do it in the fixed temperature and fixed energy pictures to explicitly proof their equivalence. We find that, at high energy, an effective two dimensional behavior appears for the number of strings. Looking at the equation of state from a ten dimensional point of view, we show that the Hagedorn behavior can be seen as correcting the Zeldovich equation of state ($\rho=p$) that can be found from the two dimensional part of the entropy of the system. By the way, we show that, near the Hagedorn temperature, the equilibrium state obtained by sharing the total energy among open (super)strings of different length is stable.