Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints
We establish a Hessian geometric structure in chemical thermodynamics, which describes chemical reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence and uniqueness condition of the equilibrium state is deriv...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033065 |
| _version_ | 1797210713684443136 |
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| author | Yuki Sughiyama Dimitri Loutchko Atsushi Kamimura Tetsuya J. Kobayashi |
| author_facet | Yuki Sughiyama Dimitri Loutchko Atsushi Kamimura Tetsuya J. Kobayashi |
| author_sort | Yuki Sughiyama |
| collection | DOAJ |
| description | We establish a Hessian geometric structure in chemical thermodynamics, which describes chemical reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence and uniqueness condition of the equilibrium state is derived by using the Legendre duality inherent to the Hessian structure. The entropy production during a relaxation to the equilibrium state can be evaluated by the Bregman divergence. Furthermore, the equilibrium state is characterized by four distinct minimization problems of the divergence, which are obtained from the generalized Pythagorean theorem originating in the dual flatness. For the ideal gas case, we confirm that our existence and uniqueness condition implies Birch's theorem, and that the entropy production represented by the divergence coincides with the generalized Kullback-Leibler divergence. In addition, under mass action kinetics, our general framework reproduces the local detailed balance condition. |
| first_indexed | 2024-04-24T10:14:58Z |
| format | Article |
| id | doaj.art-38c29ced1d8f4809bad4f78060e82dc9 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:14:58Z |
| publishDate | 2022-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-38c29ced1d8f4809bad4f78060e82dc92024-04-12T17:23:01ZengAmerican Physical SocietyPhysical Review Research2643-15642022-07-014303306510.1103/PhysRevResearch.4.033065Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraintsYuki SughiyamaDimitri LoutchkoAtsushi KamimuraTetsuya J. KobayashiWe establish a Hessian geometric structure in chemical thermodynamics, which describes chemical reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence and uniqueness condition of the equilibrium state is derived by using the Legendre duality inherent to the Hessian structure. The entropy production during a relaxation to the equilibrium state can be evaluated by the Bregman divergence. Furthermore, the equilibrium state is characterized by four distinct minimization problems of the divergence, which are obtained from the generalized Pythagorean theorem originating in the dual flatness. For the ideal gas case, we confirm that our existence and uniqueness condition implies Birch's theorem, and that the entropy production represented by the divergence coincides with the generalized Kullback-Leibler divergence. In addition, under mass action kinetics, our general framework reproduces the local detailed balance condition.http://doi.org/10.1103/PhysRevResearch.4.033065 |
| spellingShingle | Yuki Sughiyama Dimitri Loutchko Atsushi Kamimura Tetsuya J. Kobayashi Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints Physical Review Research |
| title | Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints |
| title_full | Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints |
| title_fullStr | Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints |
| title_full_unstemmed | Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints |
| title_short | Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints |
| title_sort | hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints |
| url | http://doi.org/10.1103/PhysRevResearch.4.033065 |
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