November 28, 2025 by Manuel Maidorn, Max Planck Society
Collected at: https://phys.org/news/2025-11-randomness.html
When describing collective properties of macroscopic physical systems, microscopic fluctuations are typically averaged out, leaving a description of the typical behavior of the systems. While this simplification has its advantages, it fails to capture the important role of fluctuations that can often influence the dynamics in dramatic manners, as the extreme examples of catastrophic events such as volcanic eruptions and financial market collapse reveal.
Challenges in studying complex systems
On the other hand, studying the dynamics of individual microscopic degrees of freedom comprehensively becomes too cumbersome even when considering systems of a moderate number of particles. To describe the interface between these opposite ends of the scale, stochastic field theories are commonly used to characterize the dynamics of complex systems and the effect of the microscopic fluctuations.
Due to their overwhelming complexity, predicting outcomes by analyzing these fluctuations in living or active matter systems is not possible using traditional methods of physics. Since these systems persistently consume energy, they exhibit dynamical traits that violate the laws of equilibrium thermodynamics, not unrelated to the arrow of time.
New theoretical advances in nonequilibrium systems
In recent research, Martin Johnsrud and Ramin Golestanian from the department Living Matter Physics (LMP) at MPI-DS succeeded in developing a theoretical description that can rigorously characterize the role of fluctuations in systems. “It is mathematically challenging to predict the behavior of such systems if using traditional tools from statistical mechanics,” explains Johnsrud, first author of two Letters, published in Physical Review Research.
The physicists thus developed a suitable mathematical tool to extend the existing field theories, and they are now able to make predictions about systems out of equilibrium, such as active matter. “With our formalism, we are able to define measurable quantities that can help to characterize nonequilibrium dynamics of living matter and enable experimental design of artificial active systems,” concludes Golestanian.
More information: Martin Kjøllesdal Johnsrud et al, Fluctuation dissipation relations for active field theories, Physical Review Research (2025). DOI: 10.1103/xx4z-lj5c
Martin Kjøllesdal Johnsrud et al, Fluctuation dissipation relations for the nonreciprocal Cahn-Hilliard model, Physical Review Research (2025). DOI: 10.1103/flzv-lq7x
Journal information: Physical Review Research
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