Thermodynamic inequalities under coarse-graining

到目前为止，本研究项目取得的成果涉及三个主题：第一，我们揭示了熵产生的一个几何分解(Phys。修订本E 106,024125(2022年))，对现有方法进行了改进。重要的是，它还导致了新的热力学不平等，使得相互作用的粒子系统获得了新的界限(案例研究1)。我们发现，与现有的热力学不等式相反，几何方法也允许我们获得上界，这在文献(手稿正在准备中)中至今还没有讨论过。Rev.Research 5,013017(2023年)和ARXIV：2206.14599)，使它们能够与更好地理解的连续案例(案例研究2)联系起来。我们发现，与基于Wasserstein距离的几何学(案例研究2的原始目标)不同，基于流动和力的几何学可能是有利的，因为它与热力学性质更密切相关。最后，我们在离散系统和连续系统中得到了一个新的关于熵产生与关联的不等式(ARXIV：2303.13038)。与沃瑟斯坦距离相反，沃瑟斯坦距离在连续情况下被更好地理解，这种关系以前只出现在离散系统中。这将为案例研究2的延伸提供起点(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).