Thermodynamic inequalities under coarse-graining
| Project/Area Number |
22K13974
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2022)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2024: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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| Keywords | non-equilibrium / geometry / inequalities / entropy production / ゆらぎ / 非平衡 / 統計力学 / 熱力学 |
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| Outline of Research at the Start |
Thermodynamics makes predictions about what can and cannot happen in our physical reality, which often take the form of inequalities. The present research will investigate how such inequalities depend on our knowledge about a physical system and how detailed our description of the system is.
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
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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| Strategy for Future Research Activity |
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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Report
(1 results)
Research Products
(5 results)
