Theoretical framework for engineering Boltzmann luminescent nanothermometry

Yang et al. Light: Science & Applications (2026)15:249 https://doi.org/10.1038/s41377-026-02333-2 www.nature.com/lsa NEWS & VIEWS Open Access Theoretical framework for engineering Boltzmann luminescent nanothermometry Mingzhu Yang1, Hongxin Zhang 1✉ and Fan Zhang 1✉ 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Abstract Luminescent nanothermometry based on thermally coupled levels (TCLs) has emerged as a powerful tool for noninvasive 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. Luminescent nanothermometry based on temperaturesensitive optical materials has emerged as a powerful tool for non-invasive, fast-response and high-resolution temperature sensing, showing great potential in different fields, including nanofluidics, microelectronics and biomedicine1,2. Among various techniques, ratiometric thermometry based on thermally coupled levels (TCLs) of lanthanide ions is particularly attractive. Their relative population of two closely spaced excited states follows the Boltzmann distribution, making their luminescence intensity ratio (LIR) a self-referencing and environmentally robust temperature indicator (Fig. 1, central panel)3. Boltzmann luminescent nanothermometry based on this principle has enabled a wide array of applications, from mapping temperature gradients at the sub-cellular level to providing real-time thermal feedback during in vivo photothermal therapy4,5. However, deviations between the experimental observations and the ideal Boltzmann behavior of TCLs are frequently reported6. Moreover, key operational parameters such as the temperature window for thermal coupling are often determined empirically, lacking a unified quantitative definition7. This critical gap Correspondence: Hongxin Zhang () or Fan Zhang () 1 Laboratory of Advanced Materials, College of Smart Materials and Future Energy, Department of Chemistry, New Cornerstone Science Laboratory, State Key Laboratory of Molecular Engineering of Polymers, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai, China severely restricts the practical application and standardization of TCLs-based luminescent nanothermometry. Recent years have witnessed deepening insights into the origins of these discrepancies. On one hand, factors such as the thermal distribution of Stark sublevels, interference from parasitic nonradiative relaxation channels, and nonthermal contributions to the upper-level population have been successively revealed, providing important foundations for understanding theory-experiment mismatches8,9. On the other hand, researchers have begun to explore the external conditions required for TCLs to function effectively, establishing empirical temperature windows for different thermalization energy gap (ΔE) of TCLs and investigating how factors such as host phonon energy, lanthanide-ligand distance, and transition type, influence the onset temperature of thermal equilibrium10. These works have explained why deviations occur from different perspectives and preliminarily explored how to optimize performance through material selection. However, the fundamental rules governing TCLs formation and the reliable prediction of relative sensitivity (Sr) in specific hosts remain unclear. In a recent study published in Light: Science & Applications, Fu et al. address these challenges by establishing a comprehensive theoretical framework and predictive design principles for TCLs-based nanothermometry (Fig. 1)11. This work makes three theoretical advances. Firstly, it clarifies the temperature window for effective © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Yang et al. Light: Science & Applications (2026)15:249 Page 2 of 3 Stability criterion: 'Elower≥2'E WNR ≈ WR zmann Lumin Bolt es or ce f k n r o L2 'E L1 L0 Ln3+ LIR = I1/I2 O Thermally coupled levels (TCLs) Crystal-field parameters for predicting Sr Prediction model of sensitivity (Sr) Llower I2 I1 I1 I2 'Elower high Temperature low Temperature I2 'E L1 L0 I1 Ln3+ Nd3+ Er3+ Intensity Temperature (K) Theoretical Fr am ew Nonradiative (WNR) L2 Stable thermal coupling without interference of Llower Thermal equilibrium window (WNR>>WR ) Radiative (WR) et ermom ry oth an tN Relaxation rate Definition of temperature window Sr = 6.17% K–1 based on INd/IEr Temperature (K) Two TCLs for thermometry Fig. 1 Schematic illustration of the theoretical framework for Boltzmann luminescent nanothermometry. Central panel: Fundamental principle of thermally coupled levels (TCLs) in lanthanide ions (Ln3+). Top left: Definition of the temperature window. The competition between the radiative relaxation rate (WR) and nonradiative relaxation rate (WNR) defines a temperature-critical region where thermal equilibrium is established. Top right: The stability criterion for Boltzmann coupling. To ensure stable thermal coupling without interference of the nearest lower level (Llower), the energy gap to the Llower should satisfy ΔElower ≥ 2ΔE. Bottom left: Prediction model for relative sensitivity (Sr) through crystal-field parameters. Bottom right: High-sensitivity thermometry enabled by combining two TCLs from Nd3+ and Er3+, respectively thermal coupling. By analyzing the competition between nonradiative relaxation rates (WNR) and radiative rates (WR), they define the temperature-critical region, quantifying the previously vague concept of thermal equilibrium and explaining why conventional TCLs struggle at low temperatures (Fig. 1, top left). Secondly, this work reveals the interference effect of the nearest lower level (Llower) on the (...truncated)