  Fluctuation-dissipation relation ensures thermodynamic equilibrium of a
particle immersed in a heat bath. We will show that, under certain
circumstances, the fluctuation-dissipation relation fails to ensure equilibrium
between the immersed system and the heat bath. We consider a symmetry broken
dimer, constrained to move in one dimension, is in compliance with the
requirements of fluctuation-dissipation relation. An exact analytic result
shows a nonzero average velocity of the center of mass of the dimer indicating
that the state of the system is a nonequilibrium one. Based on this new
physical observation, we propose an alternative paradigm for a Brownian motor
which would extract useful energy directly from the heat bath unlike the ones
based on Brownian Ratchet principle.
