Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion

TL;DR

This paper reveals that the thermodynamic uncertainty relation (TUR) constrains the time-scales of anomalous diffusion, such as subdiffusion and superdiffusion, in various non-equilibrium systems, linking thermodynamics with anomalous dynamics.

Contribution

It demonstrates that TUR bounds the onset of anomalous diffusion in systems like single files, polymer chains, and active models, establishing a new connection between thermodynamics and anomalous kinetics.

Findings

TUR bounds subdiffusion in single-file systems and polymer chains.

TUR constrains the onset of superdiffusion in active models.

Fluctuations in comb models become anomalous when detailed balance is broken.

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 non-equilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the time-scale 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.