The Tremor of Predictions: How Energy Dissipation Calms Randomness ✎

A shooter at the firing line fires a series of shots. The average point of impact stays the same, but the spread of the bullet holes changes depending on how much the hands tremble. In the world of random processes, fluctuations play the role of the tremor, and dissipation, that is, energy loss, plays the role of the calmer.

Researchers considered an arbitrary stochastic system, where the future state depends on the current one only with some probability. For each pair of states, one can compute the "pointwise mutual information": a measure of how well one state predicts another. It turned out that the average predictability does not depend on thermodynamic characteristics: it is determined only by the stationary distribution and the noise intensity. However, the variance of this predictability, that is, its spread along a trajectory, obeys a universal decomposition.

In linear systems, these two contributions exactly cancel each other, so energy cannot influence fluctuations. Only nonlinear forces allow dissipation to suppress the spread. Using the example of a Brownian motor on a ring, it is clear that as the nonequilibrium force increases, the fluctuations of predictability decrease monotonically and approach a lower bound set only by noise. For the Stuart-Landau stochastic oscillator, it was found that short-time accuracy and long-time coherence are governed by different mechanisms: angular velocity affects only coherence, while radial dissipation affects only fluctuations.

The work shifts the focus from average quantities to fluctuations, showing that the thermodynamic signature manifests precisely in them. This is the first universal decomposition for the variance of predictability, valid for any Langevin dynamics. The result changes the understanding of the role of dissipation: it does not create information but stabilizes its transfer, reducing the spread of predictability along a trajectory.

Now the shooter understands that the calmer does not shift the average point of impact but only reduces the tremor of the hands. In cellular sensors and control systems, this means that energy expenditure may not increase accuracy on average, but it makes accuracy more stable from attempt to attempt.