| 研究実績の概要 |
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).
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
While case study 1 has not yet been fully completed, we have made important progress in some unexpected directions (specifically, the geometric interpretation of entropy), and the publication applying these findings to the interacting particle system of case study 1 is currently being drafted.
On the other hand, we have already obtained some results regarding the relation between continuous and discrete systems, which will no doubt prove useful in the implementation of case study 2. Further, the newly derived relation between entropy production and correlations applies to both the continuous and discrete case, which will allow us to investigate the relation between the two from yet another perspective.
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| 今後の研究の推進方策 |
After finishing the publication regarding case study 1, we will move on to implement case study 2. This involves the originally planned research on the validity and tightness of the thermodynamic uncertainty relation and its relation to Wasserstein distance - this problem has in fact been partly addressed in recent research from other groups. However, as mentioned above, we recently uncovered a new type of thermodynamic inequality for correlations in both discrete and continuous systems. This offers the opportunity to investigate the relation between discrete and continuous dynamics from the viewpoint of a different type of thermodynamic inequality.
Finally, due to the cancellation of a planned conference, we used the allocated funds to already purchase the workstation necessary to start the research on case study 3, which will allow us proceed on this ahead of schedule.
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