Educing the volume out of the phase space boundary

TL;DR

The paper demonstrates that in systems with T-duality, the volume degrees of freedom are hidden on the boundary of the phase space, and the decompactification limit reveals volume dependence in the state count, with implications for string gas thermodynamics.

Contribution

It shows how volume degrees of freedom are encoded on phase space boundaries and defines the decompactification limit for string gases in a microcanonical framework.

Findings

Volume degrees of freedom are on the phase space boundary.

Decompactification limit recovers volume dependence in state counting.

Microcanonical description at finite volume is established.

Abstract

We explicitly show that, in a system with T-duality symmetry, the configuration space volume degrees of freedom may hide on the surface boundary of the region of accessible states with energy lower than a fixed value. This means that, when taking the decompactification limit (big volume limit), a number of accessible states proportional to the volume is recovered even if no volume dependence appears when energy is high enough. All this behavior is contained in the exact way of computing sums by making integrals. We will also show how the decompactification limit for the gas of strings can be defined in a microcanonical description at finite volume.