Theoretical framework for engineering Boltzmann luminescent nanothermometry

Luminescent nanothermometry based on thermally coupled levels (TCLs) has emerged as a powerful tool for non-invasive temperature sensing, but it still lacks sufficient theoretical guidelines. To address this issue, a theoretical framework for Boltzmann luminescent nanothermometry has been established, which quantitatively defines the temperature window for establishing thermal equilibrium in TCLs, establishes a practical criterion for stable thermal coupling of TCLs, and enables predictive material design of temperature sensitivity. Based on this framework, a high sensitivity of 6.17% K^-1 is achieved, providing a theoretical basis for the rational design of high-precision nanothermometers. A theoretical framework for TCLs-based luminescent nanothermometry defines the thermal equilibrium window, establishes a stability criterion and guides rational predictive design.