Performance Limits of FRIS Systems in Nakagami-$m$ Fading

Fluid reconfigurable intelligent surfaces (FRIS) have recently emerged as a promising technology for enhancing wireless link reliability through spatial decorrelation. However, their performance analysis remains challenging due to the sum-product structure of the cascaded channel. This letter develops a rigorous analytical framework for FRIS-assisted wireless systems over arbitrarily correlated Nakagami-$m$ fading channels. Specifically, we introduce a physically consistent correlation model for Nakagami-$m$ fading and derive tractable statistical characterizations for the cascaded channel. These results lead to rigorous lower bounds for the outage probability (OP), with a simplified expression also obtained for the independent and identically distributed case. To the best of our knowledge, these are the first strict OP lower bounds reported for an FRIS-aided wireless system under arbitrarily correlated Nakagami-$m$ fading. CLT- and Gamma-based approximations are included as benchmark methods. Notably, the numerical results show that the proposed OP bound not only provides rigorous performance guarantees but also yields a noticeably tighter OP characterization than the CLT approximation in the high-SNR regime.