Sense of unbalance in a dual geometric world: A novel theory for nonlinear dissipative phenomena

Losing energy is rarely a good thing, but now researchers in Japan have shown how to extend the applicability of thermodynamics to non-equilibrium systems. By geometrically encoding the energy dissipation relationships, they were able to translate the physical constraints into a generalized geometric space. This work can greatly improve our understanding of chemical reaction networks, including those underlying the metabolism and growth of living organisms.

Thermodynamics is the branch of physics concerned with the processes by which energy is transferred between entities. His predictions are of vital importance to both chemistry and biology when it comes to determining whether certain chemical reactions or interconnected reaction networks will occur spontaneously. However, while thermodynamics attempts to provide a general description of macroscopic systems, we often encounter difficulties when working on an out-of-equilibrium system. Successful attempts to extend the scope to non-equilibrium situations have usually been limited to specific systems and models.

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

In physics, duality is a central concept. Some physical entities are easier to interpret when converted to a different but mathematically equivalent representation. For example, a wave can be transformed in time to its representation in frequency space, which is its dual form. When dealing with chemical processes, thermodynamic force and flow are the nonlinearly related dual representations — their product gives the rate at which energy is lost through dissipation — in a geometric space induced by the duality, the scientists were able to show what thermodynamic relationships can look like in as well be generalized to non-equilibrium cases.

“Most previous studies of chemical reaction networks relied on assumptions about the kinetics of the system. We have shown how they can be handled more generally in the non-equilibrium case, using duality and the geometry associated with it,” says final 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 starting point for the analysis or design of complex reaction networks, such as those used in living organisms or industrial manufacturing processes.