Hessian Geometric Structure of Equilibrium and Nonequilibrium Chemical Reaction Newtworks
 Date
 September 8 (Thu) at 16:00  17:00, 2022 (JST)
 Speaker

 Tetsuya Kobayashi (Associate Professor, Institute of Industrial Science, The University of Tokyo)
 Venue
 via Zoom
 Language
 English
 Host
 Daiki Kumakura
Cells are the basic units of all living things, and their functions are realized by circuits and networks of chemical reactions. Thus, understanding the mechanism how various cellular functions are implemented by chemical reaction networks (CRN) is the central challenge in biophysics and quantitive biology. Among various aspects of CRN, its thermodynamic property is particularly important because most of biological functions are energyconsuming nonequilibrium phenomena. However, even though the equilibrium chemical thermodynamics and kinetics of chemical reactions were founded more than one century ago, the nonequilibrium theory of CRN is still immature. One reason is the nonlinearity in the constitutive equation between chemical force and flux, which prevents us from associating the tangent and cotangent spaces of the dynamics by the usual inner product structure. In this work, we show that the nonlinear relation between chemical force and flux can be captured by Legendre transformation and the geometric aspects of CRN dynamics can be characterized by Hessian geometry. Hessian geometry is the geometry generated by Legendre dual pairs of convex functions and is the basis of dually flat structure of information geometry and also equilibrium thermodynamics. Thus, we have dually flat structures in CRN dynamics, one on the statepotential space where equilibrium and energetic aspect is formulated (1,2), and the other on the forceflux space where nonequilibrium and kinetics aspect is characterized(3). Two of them are consistently connected by topological property of the underlying hypergraph structure of CRN. We discuss potential applications of this structure not only for CRN but also for other phenomena and problems(4,5).
References
 Yuki Sughiyama, Dimitri Loutchko, Atsushi Kamimura, and Tetsuya J. Kobayashi, Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints, Phys. Rev. Research 4, 033065 (2022), doi: 10.1103/PhysRevResearch.4.033065
 Tetsuya J. Kobayashi, Dimitri Loutchko, Atsushi Kamimura, and Yuki Sughiyama, Kinetic derivation of the Hessian geometric structure in chemical reaction networks, Phys. Rev. Research 4, 033066 (2022), doi: 10.1103/PhysRevResearch.4.033066
 Tetsuya J. Kobayashi, Dimitri Loutchko, Atsushi Kamimura, Yuki Sughiyama, Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions, arXiv: 2206.00863
 Yuki Sughiyama, Atsushi Kamimura, Dimitri Loutchko, Tetsuya J. Kobayashi, Chemical Thermodynamics for Growing Systems, arXiv: 2201.09417
 Dimitri Loutchko, Yuki Sughiyama, Tetsuya J. Kobayashi, Riemannian Geometry of Optimal Driving and Thermodynamic Length and its Application to Chemical Reaction Networks, arXiv: 2205.03829
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