Fisher information and fluctuations in quantum gas systems

Abstract

We revisit and synthesize the connection between Fisher information and thermodynamicfluctuations in quantum gases, focusing on the canonical and grand canonical ensembles.Building on foundational results, we compute and analyze the behavior of Fisher informationin both Bose and Fermi gases, with particular attention to its scaling near condensationtemperature 𝑇𝑐 and its sensitivity to finite-size effects. Our study clarifies how Fisher informationrelates to thermodynamic response functions and provides explicit examples demonstrating itsrole as a probe of fluctuations and coherence in quantum many-body systems. While theseconnections are known in the literature, we aim to present a self-contained and pedagogicaltreatment, supplemented with calculations that highlight how Fisher information can serve asan accessible diagnostic in the study of critical phenomena and finite-temperature effects.