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

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 $\sigma$, $P$, 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 ${\beta }_0^2=(dP\mathrm{/}d\sigma {)}_0$. For $2M<a_0<3M$, stability requires a lower bound on ${\beta }_0^2$ that diverges as $a_0\to 2M^{+}$. 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 $T_{\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}}=T_{\mathrm{a}\mathrm{c}\mathrm{c}}+O(\mathrm{\hslash }\gamma \mathrm{/}a)$, 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.