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 of the motor 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.