Systems out of equilibrium typically carry macroscopic currents of particles, mass or energy. Thermodynamic uncertainty relations offer universal bounds linking such currents and their statistical fluctuations to other system properties, especially entropy production. These bounds offer measures for analysing long-time averages, or allowing the suppression of fluctuations in biochemical reactions and molecular motors. Most previous work exploring useful forms of such relations has focussed on time-homogeneous Markovian systems, but similar relations would be valuable for a much wider class of systems, especially those with memory or history dependence.
In a new paper, LML External Fellow Rosemary Harris and Mayank Shreshtha derive a new bound for a particular class of run-and-tumble type processes, a standard paradigm for modelling bacterial motility as well as other search strategies. In such processes, random dynamics moving systematically in one direction, so-called “runs” are interrupted by stochastic resets of the preferred direction, “tumbles.” To derive bounds for such processes, the researchers use a mathematical framework based around so-called renewal-reward theory, a branch of probability theory often used in modelling inventories or the reliability of industrial processes, as well as biological systems.
As they demonstrate, the new uncertainty relation they derive for run-and-tumble models is often more restrictive and informative than previously known relations. The authors illustrate the difference in several simple single particle processes, and also with a many-particle exclusion process with collective reset. Harris and Shreshtha believe the new result could prove useful for researchers in the area of active matter.
A pre-print of the paper is available at https://arxiv.org/abs/1903.01972.
It has been accepted for publication in Europhysics Letters