# Rate dependence of current and fluctuations in jump models with negative differential mobility

## TL;DR

This paper investigates negative differential mobility in Markov jump models with traps, analyzing how different transition rates influence velocity and fluctuations, and emphasizing the importance of microscopic coarse-graining.

## Contribution

It introduces a detailed analysis of how transition rate choices affect negative differential mobility and fluctuations in jump models, highlighting the need for proper microscopic basis.

## Key findings

- Negative differential mobility depends on transition rate choices.
- Full counting statistics reveal diverse behaviors.
- Thermodynamic uncertainty relations are demonstrated.

## Abstract

Negative differential mobility is the phenomenon in which the velocity of a particle decreases when the force driving it increases. We study this phenomenon in Markov jump models where a particle moves in the presence of walls that act as traps. We consider transition rates that obey local detailed balance but differ in normalisation, the inclusion of a rate to cross a wall and a load factor. We illustrate the full counting statistics for different choices of the jumping rates. We also show examples of thermodynamic uncertainty relations. The variety of behaviours we encounter highlights that negative differential mobility depends crucially on the chosen rates and points out the necessity that such choices should be based on proper coarse-graining studies of a more microscopic description.