From Feynman's ratchet to time crystalline molecular motors.

Cats have an instinctive ability to use the connection governing parallel transport in the space of shapes to land safely on their feet. Here, we argue that the concept of connection, which is extensively used in general relativity and other parts of theoretical physics, also explains the impressive performance of molecular motors by enabling molecules to evade the conclusions of Feynman's ratchet-and-pawl analysis. First, we demonstrate the emergence of directed rotational motion from shape changes, which is independent of angular momentum. Then, we computationally design knotted polyalanine molecules and demonstrate the organization of individual atom thermal vibrations into collective rotational motion, which is independent of angular momentum. The motion occurs effortlessly even in ambient water and can be further enhanced through spontaneous symmetry breaking, rendering the molecule an effective theory time crystal. Our findings can be experimentally verified via nuclear magnetic resonance measurements and hold practical potential for molecular motor design and engineering.