The thermodynamic meaning of negative entropy

Abstract

To clarify the implications of our result, we note that, although the erasure processes we considered in our Letter can have negative work cost (that is, they can yield work), they do not violate the second law of thermodynamics, because they are not cyclic processes. A negative work cost is associated with the consumption of entanglement, which can only be restored by doing work. Our results are also consistent with the original unconditional form of Landauer's principle, which says that if there is no information available about the data being erased, the cost of erasure is always positive. Similarly, because in a computation with deterministic classical output the joint entropy of all registers conditioned on the output cannot be negative, the overall work cost of such a computation is always positive or zero (even though temporary quantum correlations may be created and exploited during the course of the computation). In fact, standard techniques of reversible information processing allow any deterministic classical algorithm to be performed, on a classical or quantum computer, in a thermodynamically reversible fashion, with work cost arbitrarily close to zero 1,2 . These clarifications are developed in more detail in the Supplementary Information to this Addendum. We thank Charles H. Bennett for remarks on reversible computation.Supplementary Information is linked to the online version of the Addendum at www.nature.com/nature.1. Bennett, C. H. The thermodynamics of computation-a review. Int. J. Theor. Phys. 21, 905-940 (1982). 2. Watrous, J. Quantum computational complexity.

Quantumness of correlations and Maxwell's demon in molecular excitations created by neutron scattering

“…This result provide a thermodynamic operational meaning for negative conditional entropy, extending earlier studies in which this negativity had found information-theoretical interpretations only. [22,23] Additionally, it has been noted [22] that the above result also indicates that quantum discord can properly quantify the difference between the work costs of erasure by using quantum or, alternatively, classical memories Q.…”

“…In the preceding derivations of quantumness of correlations, the concept of conditional entropy (or conditional information) plays a considerable role. Very recently, del Rio et al [22] showed that the standard formulation and implications of Landauers principle [40,41] are no longer valid in the presence of quantum information. Their result is that the work cost of erasure of information is determined by the entropy of the system, conditioned on the quantum information an observer has about it: the more an observer knows about the system carrying the information, the less it costs to erase the information.…”

“…The main theoretical result of Ref. [22] concerns the work, WðAjQÞ, that an observer (or demon) with access to a quantum memory Q correlated with the system A needs in order to erase the information content of A. In the thermodynamic limit, in which the observer has access to, and erases, many identical copies of A jointly, the authors have found a specific erasure process having work cost not larger than…”

“…per copy of A; see Ref. [22] for details. Quantity SðAjQÞ is the von Neumann conditional entropy, [23] SðAjQÞ5SðAQÞ2SðQÞ:…”

“…Especially, the focus is on certain surprising thermodynamical and/or energetic consequences, for instance the negative work costs for erasure of information. [22] The field "quantumness of correlations" is already enormous with an overwhelming literature (see the very recent review article [23] ). However, until now it remained rather unknown in natural sciences other than physics.…”