The cost of information erasure in atomic and spin systems

Abstract

Landauer's erasure principle, which is one of the defining elements of modern information theory, states the minimum work required to erase 1 bit of information is kT ln(2), where T is the temperature of a thermal reservoir and k is Boltzmann's constant [1]. This principle arises from the maximisation of the entropy of the whole system (memory bit plus thermal reservoir) subject to energy conservation. In this talk we explore a different kind of statistical mechanics based on more general constraints other than energy conservation. Such systems have the potential to provide new mechanisms for erasing information, initialising the state of quantum systems and providing novel "heat" engines.

We consider a gas of spin-1/2 systems (e.g. energy degenerate two-state atoms) which comes to equilibrium via angular momentum conserving interactions (e.g. elastic collisions). We model the gas as a canonical ensemble of spin particles constrained by the conservation of angular momentum. The gas acts as a spin reservoir whose macrostate is characterised by the total (fixed) average angular momentum of the gas. Our 1 bit memory device is represented by one spin-1/2 particle in an arbitrary mixed state. The state of the memory is erased by performing controlled operations on the memory particle and ancillary spin-1/2 particles and letting the memory and ancilla particles come to equilibrium with the spin reservoir. The cost of erasing 1 bit of memory is shown to be the angular momentum expended in the controlled operations. In principle there is no energy cost.

We then apply this erasure mechanism to the Maxwell's demon problem. Imagine the demon is using the hot molecules of a thermal gas to produce mechanical work and we want to erase the demon's memory. If another thermal reservoir is used for the erasure, the associated energy cost will be greater than the mechanical work extracted by the demon [2]. However, we can avoid this energy cost by using the spin-reservoir erasure mechanism. In principle, all the heat can be extracted from the thermal reservoir as mechanical work for zero energy cost. The second law of thermodynamics and energy conservation are not violated by this process. The cost is in terms of angular momentum expended and an increase in the entropy of the spin reservoir. Moreover, the entropy of the whole system is increased in the process.

[1] R. Landauer, IBM J. Res. Lett., 67 661 (1961). [2] C.H. Bennett, Int. J. Theor. Phys. 21, 905 (1982).