## I. INTRODUCTION 

A fundamental result in the thermodynamics of computation is Landauer’s erasure prin- ciple (LEP), which places a lower bound on the average heat dumped to a bath when the information in a memory device is erased. The principle holds for processes that satisfy two essential features: The process is carried out in the same way independent of the in- formation stored in the device and it restores the device to a known standard state at the end. These processes are usually known as the Landauer erasure processes. Landauer has shown that if the device holds I bits of information, then during any Landauer erasure, the average amount of heat that must be dumped to the bath is at least Ik$_{B}$T ln 2 where k$_{B}$ is Boltzmann’s constant and T is the temperature of the bath [1]. 

The principle lies at the heart of the resolution of Maxwell’s demon paradox [2–4], an important factor that stimulates continued interest on the thermodynamics of information processing. The demon has also been investigated quantum mechanically [4–7]. Also, several alternative proofs [8–11] and generalizations [12–14] of LEP have been given and different approaches aimed at quantum information processing have been developed [15, 16]. The crucial ingredient in all alternative approaches to LEP is the description of the operation on the device as a unitary transformation on a larger combined system of the device and the bath where initially the two are uncorrelated and the bath is in thermal equilibrium[23]. Unitarity of this transformation is an absolute necessity for all physical operations [17] while the noncorrelation and equilibrium assumptions are well-suited for all possible experiments. Although this viewpoint is contested [18], LEP directly follows from the unitarity: in a Landauer erasure, the transformation maps different initial device-states to the same final device-state. Since the unitary transformation has to be one-to-one, this can only happen if the state of the bath is also modified. Finally, as the bath was initially in equilibrium, changes in its state imply an increase in its energy. Exact calculations then show that the average increase in the energy of the bath must exceed the Landauer bound. 

Can there be further implications of the unitarity of the transformation on the energy exchange with the bath? A recent article gives an affirmative answer to this question for the case of processes that manipulate classical information [14]. That article presents an alternative formulation of LEP in terms of the detailed heat transfers into the bath. In this non-entropic approach, one takes the individual heats dumped to the bath for each initial 

