# Achievability of thermodynamic uncertainty relations

## TL;DR

This paper investigates the limitations of thermodynamic uncertainty relations when considering joint currents, revealing that these relations cannot be simultaneously achieved for multiple currents, which may lead to underestimating entropy dissipation.

## Contribution

It demonstrates that thermodynamic uncertainty relations cannot be simultaneously satisfied for multiple currents, highlighting a fundamental limitation in their application.

## Key findings

- Joint currents cannot satisfy thermodynamic uncertainty relations simultaneously.
- Potential underestimation of minimum entropy dissipation when using these relations.
- Highlights a fundamental limitation in current thermodynamic uncertainty frameworks.

## Abstract

The thermodynamic uncertainty relations provide a universal trade-offs between entropy dissipation rate and fluctuations in transport current. This relation has been mostly used to estimate a minimum entropy dissipation rate by experimentally measuring current fluctuations. Here we consider joint currents and show that such uncertainty relations cannot be simultaneously achievable for any two currents, which leads to a potential underestimation of the minimum entropy dissipation rate.