Before revision:  The travel distance  and its variance of motor are, however, physically constrained by energy consumption, the principle of which has recently been formulated into the thermodynamic uncertainty relation , the product between the heat dissipated from a motor and the squared relative error in the displacement, has a minimal theoretical bound (Q \geq 2 k_B T), which is approached when the time trajectory of the motor is maximally regular for a given amount of free energy input.
After revision:  The travel distance and its variance of motor are, however, physically constrained by the free energy being consumed. A recently formulated thermodynamic uncertainty relation , the product between the heat dissipated from a motor and the squared relative error in the displacement, has a minimal theoretical bound (Q \geq 2 k_B T), which is approached when the time trajectory of the motor is maximally regular for a given amount of free energy input.