Abstract
This paper investigates the finite-blocklength performance of reconfigurable holographic surfaces (RHS) for ultra-reliable low-latency communication (URLLC). A physics-consistent RHS model is established, and the information-theoretic dispersion is derived in closed form using the Mellin transform method, we derive a closed-form probability density function of the RHS-induced channel gain. Then, we apply second-order Taylor expansion and saddle point approximation to obtain analytical expressions for the mutual information and unconditional information variance, which explicitly capture the amplitude-induced anisotropic variance. Finally, leveraging the Berry-Esseen theorem, the closed-form achievability and converse bounds are established which quantify the impact of RHS design parameters, blocklength n , and average error probability ϵ on the rate. Analytical and simulation results demonstrate that RHS reduces the variance of the effective channel power by 35-50% in required blocklength compared with reconfigurable intelligent surfaces (RIS) under identical resource budgets. The findings identify RHS as a physically scalable and mathematically tractable architecture for short-packet 6G communication.