Understanding how small systems exchange energy with a heat bath is important to describe how their unique properties can be affected by the environment. In this contribution, we apply Landsberg’s theory of temperature-dependent energy levels to describe the progressive thermalization of small systems as their spectrum is perturbed by a heat bath. We propose a mechanism whereby the small system undergoes a discrete series of excitations and isentropic spectrum adjustments leading to a final state of thermal equilibrium. This produces standard thermodynamic results without invoking system size. The thermal relaxation of a single harmonic oscillator is analyzed as a model example of a system with a quantized spectrum than can be embedded in a thermal environment. A description of how the thermal environment affects the spectrum of a small system can be the first step in using environmental factors, such as temperature, as parameters in the design and operation of nanosystem properties.

中文翻译：

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热力学远远超出热力学极限

了解小型系统如何与热浴交换能量对于描述环境如何影响其独特属性非常重要。在这项贡献中，我们应用了Landsberg的温度相关能级理论来描述小型系统的渐进热化过程，因为它们的光谱受到热浴的干扰。我们提出一种机制，使小型系统经历一系列离散的激发和等熵频谱调整，从而达到热平衡的最终状态。这会产生标准的热力学结果，而无需调用系统尺寸。分析单谐波振荡器的热弛豫，作为系统的模型示例，该系统具有比可嵌入热环境中的量化频谱。