Abstract
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.
Highlights
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state
We highlight a new facet of the TUR by showing that it bounds the timescale on which a finite system can exhibit anomalous kinetics
We demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied
Summary
The situation α < 1 is referred to as subdiffusion and in a biophysical context was found in observations of particles confined to actin networks [10,11], polymers [12], denaturation bubbles in DNA [13], lipid granules in yeast [14], and cytoplasmic RNA proteins [15] In these systems subdiffusion is often thought to be a result of macromolecular crowding [16,17,18], where obstacles hinder the motion of a tracer particle. More recently out-of-equilibrium anomalous transport was studied in the context of single file diffusion in the presence of a nonequilibrium bias (v ≠ 0) [35,36,37,38] and in active comb models [see Fig. 1(c)] that were shown, quite surprisingly, to display accelerated diffusion [39] in stark contrast to passive combs At sufficiently long times where diffusion becomes normal, σ2xðtÞ ∝ t, the thermodynamic uncertainty relation (TUR) [50,51] bounds the walker’s variance by [52]
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