The thermodynamic meaning of negative entropy

Abstract

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 Here we show that the standard formulation and implications of Landauer's principle are no longer valid in the presence of quantum information.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.

Implications of Coupling in Quantum Thermodynamic Machines

“…Hence, both the cycles have the same efficiencies as shown in Equations (5) and (9). From Equations (4) and (8) …”

“…As an example, the statement of the second law of thermodynamics in the presence of an ancilla [1,2] or, when the system has coherence [3,4], has been established in great details, from where the classical version of the second law emerges under appropriate limits. The study of thermodynamics in quantum domain can be approached from different directions such as information-theoretic point of view [5][6][7][8][9][10] or resource-theoretic aspect [11][12][13]. Another important constituent, in this area of study, is the work extraction from quantum systems [14][15][16][17][18].…”

Energetic costs of cellular computation

“…biophysics | signaling | inference | nonequilibrium T he relationship between information and thermodynamics remains an active area of research despite decades of study (1)(2)(3)(4). An important implication of the recent experimental confirmation of Landauer's principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (2,3).…”

Work extraction via quantum nondemolition measurements of qubits in cavities: Non-Markovian effects

“…The balance of work and information is embodied by the Szilard-Landauer (SL) principle [1,2] whereby work obtainable from a measurement must not exceed the energy cost of erasing its record from the observer's memory. Notwithstanding ongoing efforts to expand information-based thermodynamics (IT) so as to include measurement-cost effects [10][11][12] beyond the original SL balance (see Appendix), an important aspect has been little addressed thus far [13]: How essential is the thermodynamic paradigm of system-bath separability [14,15] to the analysis of work extraction by measurements?…”

“…The balance of work and information is embodied by the Szilard-Landauer (SL) principle [1, 2] whereby work obtainable from a measurement must not exceed the energy cost of erasing its record from the observer's memory. Notwithstanding ongoing efforts to expand information-based thermodynamics (IT) so as to include measurement-cost effects [10][11][12] beyond the original SL balance (see Appendix), an important aspect has been little addressed thus far [13]: How essential is the thermodynamic paradigm of system-bath separability [14,15] to the analysis of work extraction by measurements?This question is here investigated in the context of non-Markovian quantum thermodynamics "under observation" [16][17][18][19][20][21]. Namely, we show that frequent measurements can induce changes in system-bath correlations, unaccounted for by the separability paradigm, and thereby change the tradeoff of information and work.…”