Stochastic Thermodynamics of Dynamical Thin-Shell Wormholes: Effective Temperatures, Fluctuations and Conditional Quasi-Horizon Unification

Abstract

We develop an effective stochastic and semiclassical framework for dynamical thin-shell wormholes connecting two asymptotic spacetime regions. The Israel junction geometry is separated from the phenomenological open-system description: stochastic dynamics is formulated in the radial phase space $(a,\dot a)$, whereas $σ$, $P$, and the effective temperature scales are induced observables. A one-dimensional Langevin--Fokker--Planck model is obtained only after an explicit overdamped/adiabatic approximation. Local acceleration scales are interpreted as reservoir temperatures only under additional KMS and detailed-balance assumptions. For a symmetric Schwarzschild--Schwarzschild wormhole, the transparent conservative shell defines the reference potential and restoring frequency, while dissipation and noise are introduced as open-system corrections. The stable linear response is closed by the constitutive slope $β_0^2=(dP/dσ)_0$. For $2M<a_0<3M$, stability requires a lower bound on $β_0^2$ that diverges as $a_0\to2M^+$. Moreover, the derivative along the family of static configurations equals the marginal-stability slope and must not be identified with the constitutive derivative of a stable stochastic shell. The reduced model determines stationary distributions, fluctuations, correlations, Markovian and non-Markovian spectra, and entropy production. Near the horizon, the junction conditions yield $T_{\rm stress}=T_{\rm acc}+O(\hbarγ/a)$, with equality at leading order under a specified dominance condition. A peeling temperature participates only if the ray-tracing map satisfies generalized Unruh/peeling and adiabaticity conditions. Thus, the three-temperature correspondence is conditional, while the stochastic coefficients remain phenomenological pending a microscopic shell--reservoir model.