A new theory for nonlinear dissipative phenomena

A new theory for nonlinear dissipative phenomena

X induced by the stoichiometric matrix S. The blue plane represents the stoichiometric P subspaceX(η). (b) The stoichiometric variety VY(η) (blue curved surface) obtained by P mappingX(η) in Y by the Legendre transformation ∂φ. Credit: Physical Review Research (2022). DOI: 10.1103/PhysRevResearch.4.033066″ width=”800″ height=”446″/>

(a) A linear coordinate system of X induced by the stoichiometric matrix S. The blue plane represents the stoichiometric P subspaceX(η). (b) The stoichiometric variety VY(η) (blue curved surface) obtained by P mappingX(η) in Y by the Legendre transformation ∂φ. Credit: Physical Review Research (2022). DOI: 10.1103/PhysRevResearch.4.033066

Losing energy is rarely a good thing, but now researchers in Japan have shown how to extend the applicability of thermodynamics to systems that are not in equilibrium. By encoding the energy dissipation relations in a geometric way, they were able to cast the physical constraints into a generalized geometric space. This can significantly improve our understanding of chemical reaction networks, including those that underlie the metabolism and growth of living organisms.


Thermodynamics is the branch of physics that deals with the processes by which energy is transferred between entities. Its predictions are crucial to both chemistry and biology when determining whether certain chemical reactions or interconnected networks of reactions will occur spontaneously. However, while thermodynamics tries to establish a general description of macroscopic systems, we often have difficulty working on the system out of equilibrium. Successful attempts to extend the framework to non-equilibrium situations have usually been limited to only specific systems and models.

In two studies recently published in Physical Review Research, researchers from the Institute of Industrial Science at the University of Tokyo demonstrated that complex nonlinear chemical reaction processes could be described by transforming the problem into a dual geometric representation. “With our structure, we can extend the theories of non-equilibrium systems with quadratic dissipation functions to more general cases, which are important for studying chemical reaction networks,” says first author Tetsuya J. Kobayashi.

In physics, duality is a central concept. Some physical entities are easier to interpret when they are transformed into a different but mathematically equivalent representation. For example, a wave in time space can be transformed into its representation in frequency space, which is its dual form. When dealing with chemical processes, thermodynamic force and flow are nonlinearly related dual representations—their product leads to the rate at which energy is lost to dissipation—in a duality-induced geometric space, scientists have been able to show how the relationships can thermodynamics. to be generalized even in non-equilibrium cases.

“Most previous studies of chemical reaction networks have been based on assumptions about the kinetics of the system. We have shown how these can be treated more generally in the non-equilibrium case by using duality and the associated geometry,” says last author Yuki Sughiyama. Having a more universal understanding of thermodynamic systems and extending the applicability of non-equilibrium thermodynamics to more disciplines can provide a better vantage point for the analysis or design of complex reaction networks, such as those used in living organisms or industrial manufacturing processes.


The thermodynamics of life take shape


More information:
Tetsuya J. Kobayashi et al., Kinetic Derivation of Geometric Structure Hessian in Chemical Reaction Networks, Physical Review Research (2022). DOI: 10.1103/PhysRevResearch.4.033066

Tetsuya J. Kobayashi et al., Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions, Physical Review Research (2022). DOI: 10.1103/PhysRevResearch.4.033208

Provided by the University of Tokyo

Citation: Sense of disequilibrium in a dual geometric world: A new theory for nonlinear dissipative phenomena (2022, September 16) Retrieved September 20, 2022 from https://phys.org/news/2022-09-equilibrium-dual-geometric -world-theory.html

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