Thermodynamic inequalities under coarse-graining

本研究项目目前得到的结果涉及三个主题。首先，我们发现了熵产生的几何分解（物理学）。Rev. E 106,024125(2022))，它改进了现有的方法。重要的是，它还导致了新的热力学不等式，允许获得相互作用粒子系统的新边界（案例研究1）。我们发现，与现有的热力学不等式相反，它可以被表述为耗散的下界，几何方法也允许我们获得上界，这到目前为止还没有在文献中讨论（手稿准备中）。其次，我们将这种几何方法扩展到离散空间系统（物理学）。Rev. Research 5, 013017（2023）和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，与基于Wasserstein距离的几何模型（案例研究2的原始目标）相比，基于与热力学性质更密切相关的流量和力的几何模型可能更有利。此外，这种几何结构还允许研究一类新的动力学，特别是化学反应网络。最后，我们在离散和连续系统中推导了一个新的关于熵产生与相关性的不等式（arXiv:2303.13038）。与在连续情况下更容易理解的沃瑟斯坦距离相反，这种关系以前只出现在离散系统中。这将为案例研究2的扩展提供起点（见下文）。

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).