Thermodynamic inequalities under coarse-graining

粗粒度下的热力学不等式

• 批准号: 22K13974
• 负责人: Dechant Andreas
• 金额: $ 2万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Early-Career Scientists
• 财政年份: 2022
• 资助国家: 日本
• 起止时间: 2022-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-22K13974/
• 关键词: non-equilibrium; geometry; inequalities; entropy production; ゆらぎ; 非平衡; 統計力学; 熱力学; non-equilibrium; geometry; inequalities; entropy production; ゆらぎ; 非平衡; 統計力学; 熱力学

The results obtained in this research project so far concern three topics.First, we uncovered a geometric decomposition of entropy production (Phys. Rev. E 106, 024125 (2022)), which refines existing approaches. Importantly, it also leads to new thermodynamic inequalities, allowing to obtain new bounds for interacting particle systems (case study 1). We found that, contrary to existing thermodynamic inequalities, which can be stated as lower bounds on the dissipation, the geometrical approach also allows us to obtain upper bounds, which so far have not been discussed in the literature (manuscript in preparation).Second, we extended this geometric approach to discrete-space systems (Phys. Rev. Research 5, 013017 (2023) and arXiv:2206.14599), allowing to connect them to the better understood continuous case (case study 2). We found that, instead of a geometry based on Wasserstein distance (original target for case study 2), a geometry based on the flows and forces, which is more closely related to the thermodynamic properties, may be advantageous. Moreover, this geometry also allows to investigate a new class of dynamics, specifically chemical reaction networks.Finally, we derived a new inequality relating entropy production to correlations (arXiv:2303.13038) in both discrete and continuous systems. Contrary to Wasserstein distance, which is better understood in the continuous case, such relations have previously only appeared for discrete systems. This will provide the starting point for an extension of case study 2 (see below).

到目前为止，在该研究项目中获得的结果涉及三个主题。首先，我们发现了熵生产的几何分解（Phys。Gev。E 106，024125（2022）），它完善了现有方法。重要的是，它还导致新的热力学不平等，从而获得相互作用的粒子系统的新界限（案例研究1）。我们发现，与现有的热力学不平等相反，可以将其表示为耗散的下限，几何方法还使我们能够获得上限，到目前为止尚未在文献中进行讨论（备案中的手稿）。我们将这种几何学方法扩展到了分离跨度系统（Phys。Rev.Rev. Rev. Rev. Rev. Rev. 5，01303）（20233）（20233）（20233）（2023） ARXIV：2206.14599），允许将它们连接到更好理解的连续案例（案例研究2）。我们发现，与其基于Wasserstein距离的几何形状（案例研究2的原始目标），基于流量和力的几何形状与热力学特性更紧密相关，可能是有利的。此外，这种几何形状还允许研究新的动力学类别，特别是化学反应网络。在本文中，我们在离散和连续系统中得出了将熵产生与相关性与相关性（ARXIV：2303.13038）相关的新不平等。与瓦斯汀的距离相反，在连续情况下可以更好地理解瓦斯汀的距离，此类关系以前仅出现在离散系统中。这将为扩展案例研究2的起点（见下文）。