The Hagedorn Temperature as a Nonequilibrium Dynamical Bottleneck in String Thermodynamics

Abstract

We revisit the Hagedorn regime of string theory from a nonequilibrium perspective using Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT), which formulates thermodynamic evolution directly on the state manifold without requiring a globally well-defined canonical ensemble. Treating the inverse temperature as an instantaneous, state-dependent quantity, we derive its exact scalar evolution equation, governed in the commuting limit by higher-order fluctuation moments. In an open-system extension we prove that the inverse-temperature mobility equals unity identically on the quasi-canonical family: a divergent Hagedorn variance is necessary but not sufficient for slowing-down. Sustained Hagedorn pinning requires a definite energy-injection topology, realized by a two-sector construction in which the reservoir couples only to light quasi-particle modes; the mobility then collapses, the intensive variable freezes at the Hagedorn scale, and energy condenses into the long-string sector at a finite rate. Promoting the Hagedorn scale to a moduli-dependent quantity along emergent-string limits yields a finite critical distance $\Delta_*$ beyond which pinning activates, with thermodynamic inertia diverging as $(\Delta_*-\Delta)^{a-3}$ for $1<a<3$, a thermodynamic discriminant between emergent-string and decompactification limits.