Strange kinetics of single molecules in living cells. E. Barkai, Y. Garini and R. Metzler in Physics Today 65:29 (2012).  What the paper says!?

This is a popularization paper which aims to

provide an overview of the current experimental state of single-molecule tracking in living cells.

It interests me for the difference between ensemble and time average (ergodic hypothesis):

the fundamental difference between ensemble and time averages is certainly not limited to a single observable like the mean squared displacement of a particle diffusing in living cells. Such departures from ergodicity have broad consequences for the dynamics of disordered inanimate systems, in which single-particle behavior can be very different from that of the ensemble.

Such systems provide one example of systems where each object behaves differently than the ensemble. Maybe the best illustration is how molecules in vitro behave normally, vs how they do in vivo: each with a different constant, and a different (albeit common) exponent:

It focuses on anomalous diffusion of single molecules in living cells, which has a different exponent as well as random diffusion constant from molecule to molecule. The paper is a bit technical but conveys that we're off-track of conventional dynamics and both the reasons and benefits of such departures remain unclear, besides general connections such as between «anomalous diffusion and its deep connection to ergodic principles».

There is anomalous diffusion (typically, subdiffusive) of single molecules in cells:

Anomalous diffusion of molecules in living cells is slower than normal Brownian processes.

and it is both unclear why as well as what would be the benefit of this mechanism. Maybe to leave time for things to happen... their guess looks as good as mine. It looks like evolution has taken hold of this, though:

It would seem that cells have learned ways to use subdiffusion to their advantage.

Interestingly, they can move things the other direction too:

When necessary, cells might overcome such problems by active motion along cytoskeletal motorways, along which motor proteins move cargo. Inside some long human neurons, for instance, small vesicles are transported along tubular structures for up to a meter. Such motion is “super-diffusive” in the sense that the exponent α in equation 4 exceeds 1.

The type of complications you get when dealing with living things:

A biological cell, however, is constantly changing and aging; some divide and some die. Therefore one might imagine that diffusion properties are not always invariant under time translation.