A shooter 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 trembling, and dissipation, that is, energy loss, plays the role of the steadying hand.
Scientists considered a system where the future depends on the present only with some probability. For each pair of states, one can calculate how well one predicts the other. It turned out that average predictability doesn't depend on thermodynamics: it is determined only by the stationary distribution and the noise. However, the spread of predictability follows a simple rule.
In linear systems, these two contributions cancel each other out, so energy cannot influence the spread. Only nonlinear forces allow dissipation to suppress fluctuations. It's as if the steadying hand didn't shift the average point of impact but merely reduced the trembling of the hands.
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.