通过准理想纳米气体统计模型推导热力学不确定关系中常数表达式的尝试
An Attempt to Derive the Expression of the Constant in the Thermodynamic Uncertainty Relations by a Statistical Model for a Quasi-Ideal Nano-Gas
AI总结：
本研究针对介观尺度正则对易关系中新常数β的本质问题，通过准理想纳米气体启发式模型结合经典统计物理推导其表达式，发现其理论值与实验值接近，且该常数并非新基本常数而是对应最小值。
摘要：
在近期工作中，我们已证明总熵产生、与热力学力共轭的热力学变量、以及Glansdorff-Prigogine耗散变量等基本物理量可在介观尺度下被离散化。我们已假定介观尺度下成立的正则对易关系（Canonical Commutation Rules, CCRs），且测量过程由确定与这些热力学量相关的算符本征值构成。此前工作的核心是分析这些假设带来的推论。本快报旨在理解CCRs中引入的新常数β的物理本质，具体而言仍有两个待解决的问题：β是否是一个新的基本常数？CCRs中的该常数是否对应下限？我们将从最简单的假设入手解决该问题：β的表达式可从纳米气体的一个简单模型（启发式模型）推导得出，并借助经典统计物理工具展开研究。我们将发现其理论值与实验值非常接近。我们不会对其做进一步的阐释，仅需指出：根据我们的模型，常数β似乎并非一个新的基本常数，而是对应最小值。
英文摘要：
In recent work, we have shown that fundamental quantities such as the total entropy production, the thermodynamic variables conjugate to the thermodynamic forces, and the Glansdorff-Prigogine's dissipative variable may be discretized at the mesoscopic scale. The Canonical Commutation Rules (CCRs) valid at the mesoscopic scale have been postulated and the measurement process consists of determining the eigenvalues of the operators associated with the thermodynamic quantities. The essence of that work was to analyze the consequences of these postulates. This letter aims to understand the physical nature of the new constant (beta) introduced in the CCRs. In particular, two questions are still open. Is beta a new fundamental constant? Does the constant in the CCRs correspond to the lowest limit? We shall tackle the problem starting from the simplest assumption: the expression of beta can be derived from a simple model (a heuristic model) for nano-gas and studied through the tools of classical statistical physics. We will find that the theoretical value is very close to the experimental one. We shall not go further in our interpretation; we shall limit ourselves simply by noticing that according to our model, the constant beta does not appear to be a new fundamental constant but corresponds to the minimum value.
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