Thermodynamic uncertainty relations and molecular-scale energy conversion

The thermodynamic uncertainty relation (TUR) is a universal constraint for nonequilibrium steady states that requires the entropy production rate to be greater than the relative magnitude of current fluctuations. It has potentially important implications for the thermodynamic efficiency of molecular-scale energy conversion in both biological and artificial systems. An alternative multidimensional thermodynamic uncertainty relation (MTUR) has also been proposed. In this paper we apply the TUR and the MTUR to a description of molecular-scale energy conversion that explicitly contains the degrees of freedom exchanging energy via a time-independent multidimensional periodic potential. The TUR and the MTUR are found to be universal lower bounds on the entropy generation rate and provide upper bounds on the thermodynamic efficiency. The TUR is found to provide only a weak bound while the MTUR provides a much tighter constraint by taking into account correlations between degrees of freedom. The MTUR is found to provide a tight bound in the near or far from equilibrium regimes but not in the intermediate force regime. Collectively, these results demonstrate that the MTUR is more appropriate than the TUR for energy conversion processes, but that both diverge from the actual entropy generation in certain regimes.