above expression, we see that with a positive β the system will move towards left i.e. in the direction from x$_{1}$ to x$_{2}$ and it changes sign with the change in sign of β . This selection of the direction of motion can easily be understood. The effective spring constant for the particle at x$_{1}$ being α/ (1 − β ) is greater than α for a positive β . As a result the particle at x$_{1}$ will impinge on the particle at x$_{2}$ with more momentum and that will make the system move towards left. The situation will change with the change in the sign of β . A calculation of the efficiency of the system is quite straight forward. Considering the average input energy to the system is proportional to < ˙ X 2 > (i.e. average instantaneous kinetic energy of the CM), we can take the effective energy output as < ˙ X > $^{2}$. Now, the efficiency can be given as η$_{eff}$ = < ˙ X > 2 / < ˙ X 2 > . The explicit calculation produces Some interesting features can immediately be found out from the above relation for the efficiency. The efficiency being not dependent on the temperature it explicitly shows that the thermal energy is not being drained out. But, it is helping the system achieve directional transport because, the average velocity of the CM is a function of temperature. This explicit non-dependence of the efficiency on temperature is an important feature. The maximum efficiency (for β = 1) is 100 × 2 /π which is roughly 64%. This is a big percentage efficiency indeed. The efficiency goes linearly to zero with α and with β . To compare the analytic results we simulate the system. While simulating the system, to apply the volume exclusion i.e. correcting for particle positions when they cross each other during sequential updating we work at two extreme limits namely particles suffering totally elastic and inelastic collisions. In the totally elastic collision scheme, we swap the particle positions following any violation of the volume exclusion and thus the CM remains unaltered preserving the momentum. In the totally inelastic scheme, we place the particles at the CM following any violation of the volume exclusion constraint. In Fig.1a and b we have plotted the average velocity of the system against α and β respectively at some constant value of the other parameters. During these simulations we have kept the strength of the thermal noise < η 2 > = 2 T = 0 . 0001. In all the simulations we have taken the maximum positive value for β to be 0.99 because the average velocity of the system diverges at β = 1. In Fig.2a and b we have plotted the efficiency of the system against the parameters α and β as well under similar situations. In these figures a comparison of simulation results with η$_{eff}$ = 1 π $_{2}$[1 + 2(1 $_{−}$β )(2 $_{−}$β ) αβ 2 ] . (7) 5