Abstract The Q10 temperature coefficient, which is widely used in scientific literature, is a measure of the temperature sensitivity of chemical reaction rates or biological processes. However, the conclusions drawn from applying this coefficient to experimental data obtained from biological processes are not universal. In many biological processes, Q10 values are often discordant with the results predicted by the Arrhenius law. The hypothesis tested in the present study is that this problem arises mainly from the fact that the Q10 coefficient is defined by the ratio between rates described by exponential laws instead of power laws. Considering this hypothesis and the need to review the mathematical laws and models currently used to describe rates and Q10 coefficients, we propose a model beyond the usual Arrhenius theory or exponential decay law herein. The proposed mathematical model is based on the theory of deformed exponential functions, with the ordinary Q10 model representing the conventional exponential function. Therefore, all results following the standard model remain valid. Moreover, we include a Q10 free open-source code, written in Python, and compatible with Windows, Linux and macOS platforms. The validation of the proposed model and confirmation of the given hypothesis were performed based on the following temperature-dependent biological processes: soil organic carbon (SOC) decomposition (which is essential to forecast the impact of climate change on terrestrial ecosystems); the metabolism of Arctic zooplankton; physiological processes of the respiratory and cardiovascular systems; rate of oxygen consumption in mitochondria of the eurythermal killifish Fundulus heteroclitus, and leaf respiration.

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温度系数（Q10）及其在生物系统中的应用：超越阿伦尼乌斯理论

摘要 Q10 温度系数在科学文献中广泛使用，是衡量化学反应速率或生物过程的温度敏感性的指标。然而，将该系数应用于从生物过程获得的实验数据得出的结论并不普遍。在许多生物过程中，Q10 值往往与阿伦尼乌斯定律预测的结果不一致。在本研究中检验的假设是，这个问题主要源于这样一个事实，即 Q10 系数是由指数定律而不是幂定律描述的比率之间的比率定义的。考虑到这一假设以及需要审查当前用于描述比率​​和 Q10 系数的数学定律和模型，我们在这里提出了一个超越通常的阿伦尼乌斯理论或指数衰减定律的模型。提出的数学模型基于变形指数函数理论，普通的 Q10 模型代表常规指数函数。因此，所有遵循标准模型的结果仍然有效。此外，我们还包含 Q10 免费开源代码，用 Python 编写，并与 Windows、Linux 和 macOS 平台兼容。所提出模型的验证和给定假设的确认是基于以下依赖于温度的生物过程进行的：土壤有机碳 (SOC) 分解（这对于预测气候变化对陆地生态系统的影响至关重要）；北极浮游动物的新陈代谢；呼吸系统和心血管系统的生理过程；