Carbonate clumped isotopes (${\mathrm{\Delta }}_{47}$) have become a widely applied method for paleothermometry, with applications spanning many environmental settings over hundreds of millions of years. However, ${\mathrm{\Delta }}_{47}$-based paleothermometry can be complicated by closure temperature-like behavior whereby C–O bonds are reset at elevated diagenetic or metamorphic temperatures, sometimes without obvious mineral alteration. Laboratory studies have constrained this phenomenon by heating well-characterized materials at various temperatures, observing temporal ${\mathrm{\Delta }}_{47}$ evolution, and fitting results to kinetic models with prescribed C–O bond reordering mechanisms. While informative, these models are inflexible regarding the nature of isotope exchange, leading to potential uncertainties when extrapolated to geologic timescales. Here, we instead propose that observed reordering rates arise naturally from random-walk ${}^{\mathrm{18}}\mathrm{O}$ diffusion through the carbonate lattice, and we develop a “disordered” kinetic framework that treats C–O bond reordering as a continuum of first-order processes occurring in parallel at different rates. We show theoretically that all previous models are specific cases of disordered kinetics; thus, our approach reconciles the transient defect/equilibrium defect and paired reaction-diffusion models. We estimate the rate coefficient distributions from published heating experiment data by finding a regularized inverse solution that best fits each ${\mathrm{\Delta }}_{47}$ timeseries without assuming a particular functional form a priori. Resulting distributions are well-approximated as lognormal for all experiments on calcite or dolomite; aragonite experiments require more complex distributions that are consistent with a change in oxygen bonding environment during the transition to calcite. Presuming lognormal rate coefficient distributions and Arrhenius-like temperature dependence yields an underlying activation energy, E, distribution that is Gaussian with a mean value of ${\mu }_E=224.3\pm 27.6$ kJ mol⁻¹ and a standard deviation of ${\sigma }_E=17.4\pm 0.7$ kJ mol⁻¹ ($\pm 1\sigma$ uncertainty; $n=24$) for calcite and ${\mu }_E=230.3\pm 47.7$ kJ mol⁻¹ and ${\sigma }_E=14.8\pm 2.2$ kJ mol⁻¹ ($n=4$) for dolomite. These model results are adaptable to other minerals and may provide a basis for future experiments whereby the nature of carbonate C–O bonds is altered (e.g., by inducing mechanical strain or cation substitution). Finally, we apply our results to geologically relevant heating/cooling histories and suggest that previous models underestimate low-temperature alteration but overestimate ${\mathrm{\Delta }}_{47}$ blocking temperatures.

碳酸盐成簇的同位素（${\mathrm{\Delta }}_{47}$）已成为古温度计的一种广泛应用的方法，其应用跨越了数亿年的许多环境设置。然而，${\mathrm{\Delta }}_{47}$基的古温度计可能会因类似闭合温度的行为而复杂化，因为在高温成岩或变质温度下，C–O键会重置，有时不会发生明显的矿物变化。实验室研究通过在各种温度下加热特性良好的材料并观察时间来限制了这种现象。${\mathrm{\Delta }}_{47}$演化，并将结果拟合到具有规定的C-O键重排机制的动力学模型。这些模型虽然内容丰富，但对于同位素交换的性质却不灵活，因此在推断到地质时标时会导致潜在的不确定性。在这里，我们建议观察到的重新排序率自然来自随机游走${}^{\mathrm{18岁}}\mathrm{Ø}$通过碳酸盐晶格扩散，我们建立了一个“无序”动力学框架，该构架将C-O键重排视为一阶过程的连续体，并以不同的速率并行发生。从理论上讲，我们证明所有先前的模型都是无序动力学的特定情况；因此，我们的方法调和了瞬态缺陷/平衡缺陷和成对的反应扩散模型。我们通过找到最适合每种条件的正则化逆解来估计已发布的加热实验数据中的速率系数分布${\mathrm{\Delta }}_{47}$不假定特定功能先验的时间序列。对于方解石或白云石的所有实验，所得分布均很好地近似为对数正态分布。文石实验需要更复杂的分布，这与向方解石过渡期间氧键合环境的变化相一致。假设对数正态速率系数分布和类似阿伦尼乌斯的温度相关性，会产生一个潜在的活化能E E分布，该分布为高斯分布，平均值为${\mu }_E=224.3\pm 27.6$kJ  mol ^-1和标准偏差为${\sigma }_E=17.4\pm 0.7$kJ 摩尔^-1（$\pm \mathrm{1个}\sigma$ 不确定; $ñ=24$）方解石和 ${\mu }_E=230.3\pm 47.7$kJ  mol ^-1和${\sigma }_E=14.8\pm 2.2$kJ 摩尔^-1（$ñ=4$）用于白云石。这些模型结果可适用于其他矿物，并可能为将来的实验提供基础，从而改变碳酸盐C–O键的性质（例如，通过引起机械应变或阳离子取代）。最后，我们将我们的结果应用于地质相关的加热/冷却历史，并建议以前的模型低估了低温变化，但高估了${\mathrm{\Delta }}_{47}$ 阻止温度。