Achievability of thermodynamic uncertainty relations

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.