(a) a linear coordinate system of *X* induced stoichiometric matrix *s*. The blue plane represents the stoichiometric subspace P^{X}(η). (b) The stoichiometric manifold V.^{s}(η) (blue curved surface) obtained by designating P^{X}(η) to Y by Legendre ∂φ transformation. attributed to him: *Physical Review Research* (2022). DOI: 10.1103/ PhysRevResearch.4.033066

Energy loss is rarely a good thing, but now, researchers in Japan have shown how to extend the application of thermodynamics to non-equilibrium systems. By encoding the energy dissipation relationships in a geometric way, they were able to cast physical constraints into a generalized geometric space. This work may greatly improve our understanding of chemical reaction networks, including those that underlie the metabolism and growth of organisms.

Thermodynamics is the branch of physics that deals with the processes by which energy is transferred between entities. His predictions are crucial to both chemistry and biology when determining whether they are certain chimical interaction, or networks of interconnected interactions, will continue automatically. However, while Thermodynamics It attempts to create a general description of macroscopic systems, and we often have difficulties working on the system out of equilibrium. Successful attempts to extend the framework to imbalances are usually limited only to specific systems and models.

In two studies recently published in *Physical Review Research*, researchers from the University of Tokyo’s Institute of Industrial Sciences have shown that complex nonlinear chemical reaction processes can be described by transforming the problem into a double geometric representation. First author Tetsuya J.

In physics, duality is a central concept. Some physical entities are easier to interpret when converted to a different, but mathematically equivalent, representation. As an example, a wave in time space can be converted to its representation in frequency space, which is its double form. when dealing with chemical processesThermodynamic force and flow are the two related nonlinear representations—their product leads to the rate of energy loss of dissipation—in geometric space caused by duality, the scientists were able to show how thermodynamic relationships can be generalized even in non-equilibrium states.

“Most of the previous studies of chemical reaction networks relied on assumptions about the kinetics of the system,” says recent author Yuki Sugiyama. “We showed how they can be handled in general at non-equilibrium through the use of duality and associated geometry.” Having a more comprehensive understanding of thermodynamic systems, and extending the application of non-equilibrium thermodynamics to more disciplines, could provide a better point for analyzing or designing complex interaction networks, such as those used in living organisms or industrial manufacturing processes.

**more information:**

Tetsuya J. Kobayashi et al, Kinetic derivation of the Hessian geometric structure in chemical reaction networks,

*Physical Review Research*(2022). DOI: 10.1103/ PhysRevResearch.4.033066

Tetsuya J. Kobayashi et al, Hessian engineering of non-equilibrium chemical reaction networks and entropy production decomposition, *Physical Review Research* (2022). DOI: 10.1103/ PhysRevResearch.4.033208

Introduction of

University of Tokyo

**the quote**: Sense of imbalance in a dual geometric world: a new theory of nonlinear commutative phenomena (2022, September 16) Retrieved on September 18, 2022 from https://phys.org/news/2022-09-equilibrium-dual-geometric-world- theory.html

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