2025/11/07 by Meng, Ye-Ming, Shi, Zhe-Yu · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2511.05042
openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28
Uncertainty relations represent a foundational principle in quantum mechanics, imposing inherent limits on the precision with which mechanically conjugate variables such as position and momentum can be simultaneously determined. This work establishes analogous relations for thermodynamically conjugate variables -- specifically, a classical intensive parameter θ and its corresponding extensive quantum operator O -- in equilibrium states. We develop a framework to derive a rigorous thermodynamic uncertainty relation for such pairs, where the uncertainty of the classical parameter θ is quantified by its quantum Fisher information Fθ. The framework is based on an exact integral representation that relates Fθ to the autocorrelation function of operator O. From this representation, we derive a tight upper bound for the quantum Fisher information, which yields a thermodynamic uncertainty relation: Δθ ΔO ≥ kBT with ΔO≡∂θ⟨O⟩ Δθ and T is the system temperature. The result establishes a fundamental precision limit for quantum sensing and metrology in thermal systems, directly connecting it to the thermodynamic properties of linear response and fluctuations.