Thermodynamics of 2D string theory

TL;DR

This paper analyzes the thermodynamic properties of 2D string theory using matrix quantum mechanics, revealing consistent thermodynamics and non-zero entropy in a tachyon-perturbed background.

Contribution

It provides a detailed calculation of free energy, energy, and entropy in 2D string theory with tachyon perturbations, connecting microscopic results to thermodynamic relations.

Findings

System exhibits thermodynamic behavior at temperature T=1/(2πR)

Microscopic energy satisfies thermodynamic relations

System has non-zero entropy

Abstract

We calculate the free energy, energy and entropy in the matrix quantum mechanical formulation of 2D string theory in a background strongly perturbed by tachyons with the imaginary Minkowskian momentum $\pm i/R$ (``Sine-Liouville'' theory). The system shows a thermodynamical behaviour corresponding to the temperature $T=1/(2\pi R)$. We show that the microscopically calculated energy of the system satisfies the usual thermodynamical relations and leads to a non-zero entropy.