Adventures in Thermal Duality (II): Towards a Duality-Covariant String Thermodynamics

TL;DR

This paper develops a duality-covariant thermodynamics framework for string theory, modifying traditional entropy and heat definitions to respect thermal duality symmetry, with implications for high-temperature behavior and holography.

Contribution

It introduces a new formulation of thermodynamics in string theory that maintains thermal duality symmetry in all key thermodynamic quantities.

Findings

Modified entropy can be smaller than standard entropy at high temperatures.

Corrections to thermodynamic quantities are suppressed by powers of the string scale.

Potential connection between entropy behavior and the holographic principle.

Abstract

In a recent companion paper, we observed that the rules of ordinary thermodynamics generally fail to respect thermal duality, a symmetry of string theory under which the physics at temperature T is related to the physics at the inverse temperature 1/T. Even when the free energy and internal energy exhibit the thermal duality symmetry, the entropy and specific heat are defined in such a way that this symmetry is destroyed. In this paper, we propose a modification of the traditional definitions of these quantities, yielding a manifestly duality-covariant thermodynamics. At low temperatures, these modifications produce "corrections" to the standard definitions of entropy and specific heat which are suppressed by powers of the string scale. These corrections may nevertheless be important for the full development of a consistent string thermodynamics. We find, for example, that the string-corrected entropy can be smaller than the usual entropy at high temperatures, suggesting a possible connection with the holographic principle. We also discuss some outstanding theoretical issues prompted by our approach.