Directional fidelity of nanoscale motors and particles is limited by the second law of thermodynamics via a universal equality

TL;DR

This paper establishes a universal equality linking the directional fidelity of nanoscale motors to the minimum energy required, demonstrating that the second law of thermodynamics fundamentally limits their efficiency.

Contribution

The authors derive a universal fidelity-energy equality for nanoscale motors, validated by experiments, revealing the thermodynamic limit on directional motion at the nanoscale.

Findings

Experimental validation with biological nanomotors supports the equality.

Biological nanomotors operate near the thermodynamic efficiency limit.

The second law sets a fundamental energy cost for directional motion.

Abstract

Directional motion of nanoscale motors and driven particles in an isothermal environment costs a finite amount of energy despite zero work as decreed by the 2nd law, but quantifying this general limit remains difficult. Here we derive a universal equality linking directional fidelity of an arbitrary nanoscale object to the least possible energy driving it. The fidelity-energy equality depends on the environmental temperature alone; any lower energy would violate the 2nd law in a thought experiment. Real experimental proof for the equality comes from force-induced motion of biological nanomotors by three independent groups for translational as well as rotational motion. Interestingly, the natural self-propelled motion of a biological nanomotor (F1-ATPase) known to have nearly 100% energy efficiency evidently pays the 2nd-law decreed least energy cost for direction production.