Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

In 1929, Leó Szilárd invented a feedback protocol1 in which a hypothetical intelligence—dubbed Maxwell’s demon—pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon’s role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy2–6. An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using realtime feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality7, and suggests a new fundamental principle of an ‘information-to-heat engine’ that converts information into energy by feedback control. To illustrate the basic idea of our feedback protocol, let us consider a microscopic particle on a spiral-staircase-like potential (Fig. 1). We set the height of each step comparable to the thermal energy kBT , where kB is the Boltzmann constant and T is temperature. Subjected to thermal fluctuations, the particle jumps between steps stochastically. Although the particle sometimes jumps to an upper step, downward jumps along the gradient are more frequent than upward jumps. In this manner, on average, the particle falls down the stairs unless it is externally pushed up (Fig. 1a). Now, let us consider the following feedback control: We measure the particle’s position at regular intervals, and if an upward jump is observed we place a block behind the particle to prevent subsequent downward jumps (Fig. 1b). If this procedure is repeated, the particle is expected to climb up the stairs. Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. In such a case, what drives the particle to climb up the stairs? This apparent contradiction to the second law of thermodynamics, epitomized by Maxwell’s demon, inspired many physicists to generalize the principles of thermodynamics1,5,6. It is now understood that the particle is driven by the ‘information’ gained by the measurement of the particle’s location5,8. In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant but