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Oxford University Press eBooks

The Nernst Postulate: the Third Law of Thermodynamics

Robert H. Swendsen

Published Mar 1, 2012• 0 citations
Publisher

Abstract

The Nernst postulate (third law of thermodynamics) puts a lower bound on entropy, which is a consequence of the quantum laws of nature. This chapter discusses the thermodynamic consequences of the Nernst postulate.
DOI
10.1093/acprof:oso/9780199646944.003.0018

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The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near to absolute zero. On the other hand, a fundamental assumption of quantum computing is to start each computation from a register of qubits initialized in a pure state, i.e., at zero temperature. These conflicting aspects, at the interface between quantum computing and thermodynamics, are often overlooked or, at best, addressed only at a single-qubit level. In this Letter, we argue how the existence of a small but finite effective temperature, which makes the initial state a mixed state, poses a real challenge to the fidelity constraints required for the scaling of quantum computers. Our theoretical results, carried out for a generic quantum circuit with N-qubit input states, are validated by test runs performed on a real quantum processor.
Thermodynamics, the branch of physics concerned with the description of macroscopic bodies, heat exchange and the conversion of different forms of energy is based on four laws: the zeroth law, which states that bodies in thermal contact reach a state of thermal equilibrium, the first law, which postulates the energy conservation and establishes the way in which different forms of energy transform into each-other, the second law, which states that the entropy increases or stays constant in time in any isolated system, and, finally, the third law (or Nernst postulate), which states that the entropy of any system approaches a constant minimum when temperature approaches 0 K. One of the direct consequences of the third law is that the specific heat of any system converges to zero when its temperature decreases to zero Kelvins. Here we show that the third law is violated in a wide class of fermionic systems, by calculating the specific heat and showing that it diverges to infinity when the absolute zero temperature is approached. Until now, no exception to these four laws is know in physics. These findings ask for the revision of one of the most fundamental laws of nature.
Thermodynamics is a meta-theory describing rules of natural behavior to which all microscopic physical theories have to conform. Physicists have used it to derive many, at first sight unrelated, results, such as Einstein's general relativity \\cite{jacobson} or the quantum hypothesis \\cite{einstein}. It is natural to ask whether quantum entanglement - a phenomenon in which two or more quantum systems have to be described with reference to each other \\cite{schroedinger} - can be based on thermodynamics. Here we show that the universal validity of the Third Law of Thermodynamics \\cite{nernst} relies on the existence of quantum entanglement. This is because without it heat capacity would diverge in general in the limit of very low temperatures, in contrast to the Third Law of Thermodynamics. Our result implies that heat capacity, although a macroscopic property, can be used to detect entanglement. This can be of a great importance for emerging quantum information technology \\cite{nielsen}.}