Thermodynamic inequalities under coarse-graining

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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).