The thermodynamic meaning of negative entropy

By Lídia del Rio, Johan Aberg, Renato Renner, Oscar C. O. Dahlsten, Vlatko Vedral. Nature, 2010

384 citations recorded by the source corpus.

The heat generated by computations is not only an obstacle to circuit miniaturization but also a fundamental aspect of the relationship between information theory and thermodynamics. In principle, reversible operations may be performed at no energy cost; given that irreversible computations can always be decomposed into reversible operations followed by the erasure of data, the problem of calculating their energy cost is reduced to the study of erasure. Landauer’s principle states that the erasure of data stored in a system has an inherent work cost and therefore dissipates heat. However, this consideration assumes that the information about the system to be erased is classical, and does not extend to the general case where an observer may have quantum information about the system to be erased, for instance by means of a quantum memory entangled with the system. Here we show that the standard formulation and implications of Landauer’s principle are no longer valid in the presence of quantum information. Our main result is that the work cost of erasure is determined by the entropy of the system, conditioned on the quantum information an observer has about it. In other words, the more an observer knows about the system, the less it costs to erase it. This result gives a direct thermodynamic significance to conditional entropies, originally introduced in information theory. Furthermore, it provides new bounds on the heat generation of computations: because conditional entropies can become negative in the quantum case, an observer who is strongly correlated with a system may gain work while erasing it, thereby cooling the environment.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b082233b2d7c38a7e1aa18beddfdd6af9e087abd

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Citations in the corpus

Thermodynamics of quantum systems under dynamical control (2015, methodology): “…by mere observation of the system, unless some action is taken (by a “demon”) pursuant to the observation (Caves, 1990; Deffner and Jarzynski, 2013; Del Rio et al., 2011; Jacobs, 2012; Landauer, 1961; Maruyama et al., 2009; Moore and Scully, 1986; Scully, 2001; Szilard, 1929; Toyabe et al., 2010).”
Quantum thermodynamics (2015, background): “The possibility to extract work during erasure is a purely quantum feature that relies on accessing the side-information [8].”
Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures (2015, background): “This study includes dynamical analysis of engines and refrigerators in the quantum regime [1,14,16–40], theoretical frameworks that take into account single-shot events [41,42], and the study of thermalization mechanisms [43–45].”
Exponential Decay of Correlations Implies Area Law (2012, neutral): “[67, 68] for other examples).”
Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions (2016, background): “In the presence of initial correlations, it is well known that Landauer’s bound does not hold [49,124,125].”
The second laws of quantum thermodynamics (2013, background): “In particular, this can occur when resetting a memory register to a pure state, while retaining the state of a reference system (11, 12).”
The role of quantum information in thermodynamics—a topical review (2015, background): “It was shown [78, 81] that the optimal work cost of that transformation is approximately H S M k T ln 2 max B ( ∣ )  r , where ò parametrizes our error tolerance and H S M max ( ∣ )  r is the smooth max entropy, a conditional entropy measure that measures our uncertainty about the state of S, give”