The work sits off to the side: its closest neighbors study the link between dissipation and precision in biological systems, for example through thermodynamic uncertainty relations or information flows in biochemical networks. However, these approaches deal in averages, such as mutual information or information transfer rate. The authors shift the focus to fluctuations in predictability along individual trajectories, which opens a new layer of thermodynamic control that is invisible in the averages.
The authors considered arbitrary Langevin dynamics and computed the moment-generating function for the pointwise mutual information between states separated by a short time lag. In the short-time limit, the propagator becomes Gaussian, which allowed them to obtain an analytical expression for the variance of predictability. This expression includes three contributions: a noise term, a geometric term (the varientropy of the stationary distribution), and a thermokinetic term that depends on the entropy production rate and dynamic activity (traffic).
The main result: the variance of the pointwise mutual information decomposes into a sum of contributions from noise, the geometry of the stationary distribution, and thermokinetic factors. The entropy production rate enters with a negative sign, meaning that dissipation suppresses fluctuations in predictability, while traffic can amplify them. The average predictability (mutual information) does not depend on thermodynamics and is determined only by the stationary distribution and diffusion. In linear systems, the thermodynamic and kinetic contributions cancel exactly, so dissipative control of fluctuations is possible only in the presence of nonlinearities. Using the example of a Brownian motor on a ring, it is shown that as the nonequilibrium force grows, the fluctuations in predictability decrease monotonically and approach a lower bound set by noise alone. For the Stuart-Landau stochastic oscillator, it was found that short-time precision (suppression of fluctuations) and long-time coherence (the number of oscillations before phase loss) are governed by different mechanisms: angular velocity affects only coherence, while radial dissipation affects only the fluctuations.
The work differs from its neighbors in that it considers not average information but its fluctuations, and shows that the thermodynamic signature appears precisely in them. This is the first universal decomposition for the variance of predictability, valid for any Langevin dynamics. The result changes the picture of dissipation's role: it does not create information but stabilizes its transfer, reducing the spread of predictability along a trajectory.
A natural continuation is to extend the theory to discrete Markov processes and chemical master equations, which would make it possible to describe biochemical networks. Another direction is to study fluctuations of information during transfer between different observables, for example between an input signal and the response of a sensory system. This could reveal new constraints on the precision of biological processes.
The results are applicable to the design of energy-efficient control systems, where it is important to minimize the spread of the response under a limited energy budget. In biology, they provide a basis for understanding how cells ensure reliable signal transmission at low cost.
Test the decomposition on discrete models, such as chemical master equations, and investigate information fluctuations between an input signal and the response of a subsystem.
The work is directly connected to the unsolved problem of the thermodynamic cost of precise information transfer in biological systems. It shows that to understand reliability, one must take into account not only averages but also fluctuations in predictability, which are controlled by dissipation and dynamic activity.
In linear systems, dissipation and dynamic activity always cancel each other, so fluctuations in predictability do not depend on how far from equilibrium the system is. Only nonlinear forces allow energy to influence the reliability of information transfer.