Press Releases

DATE2023.08.23 #Press Releases

Understanding nature’s design principles using non-equilibrium thermodynamics

Physicists unveiled the universal law relating cross-correlation function and thermodynamic driving force.

Aug 23, 2023

Many processes in nature need a thermodynamic driving force, which provides energy to the system. The driving force can be chemical, mechanical, or electrical energy. Naruo Ohga, Sosuke Ito, and Artemy Kolchinsky of the University of Tokyo have discovered a universal trade-off between the thermodynamic driving force and the cross-correlation function. Based on the trade-off relationship, they also resolved a conjecture that baffled the scientific field for six years.

The cross-correlation function reflects how two quantities interact over time. In an equilibrium system, the cross-correlation function has a constraint called microscopic reversibility. For example, in equilibrium, a chemical transition from one state to another must occur just as frequently as the reverse transition. The cross-correlation function must be symmetric due to this microscopic reversibility.

There is a significant macroscopic consequence of microscopic reversibility: the Onsager reciprocal relations. For example, heat flows from warmer to colder parts, as fluids flow from high-pressure to low-pressure areas, so the system attains equilibrium at the end of it.  When both pressure and temperature vary, the pressure difference can lead to heat flow and vice versa. According to microscopic reversibility and Onsager reciprocal relations, heat and fluid flow changes must be the same degree in a near-equilibrium state.

Image. Left: Cross-correlations between two quantities. Right: Universal constraint on cross-correlation functions.

The physicists now revealed a universal constraint on cross-correlation function in a non-equilibrium steady state. In a non-equilibrium steady state, a system does not reach equilibrium at the end of reaction. Such states are common in living systems. For instance, non-equilibrium dynamics of cell membrane transport maintain an ion concentration difference between the outside and inside cells due to the thermodynamic driving force acting on the system.

An essential quantity that characterizes non-equilibrium phenomena is the asymmetry of cross-correlations. The asymmetry in cross-correlations defines how much the value of cross-correlation changes when the order in which the two quantities are measured is reversed. “We now found a simple relation between the asymmetry of cross-correlations and the thermodynamic driving force,” says Sosuke Ito, an Associate Professor at the School of Science.

Microscopic reversibility and its macroscopic consequence, such as the Onsager reciprocal relations, have applications in various scientific fields. So, the finding opens a new way in various scientific fields to evaluate a thermodynamic driving force by experimentally measuring the cross-correlations and deriving limits for various non-equilibrium phenomena in terms of driving forces. It thus leads to a unified understanding of non-equilibrium phenomena such as in living systems.

For more details, please refer to the publication:

Naruo Ohga, Sosuke Ito, and Artemy Kolchinsky. Thermodynamic bound on the asymmetry of cross-correlations. 2023. Physical Review Letters. DOI: 10.1103/PhysRevLett.131.077101