Authors: Oleg Kupervasser
The paper of D. Jennings, T. Rudolph (the authors) "Entanglement ..." is very interesting. But the Thermodynamic Arrow of Time is not applicable for microsystems. It is a nice paper about quantum fluctuation, but not a paper about Thermodynamic Arrow of Time. In the Abstract of the paper “Entanglement ...” the authors write: "We examine in detail the case of three qubits, and also propose some simple experimental demonstrations possible with small numbers of qubits." But no thermodynamics is possible for such a microsystem. The authors (like Maccone) don't understand that categories "thermodynamic arrow of time", “macroscopic thermodynamic entropy” are correct only for large macrosystems. Using these categories for small fluctuating systems has no physical sense. We give (instead of Maccone) the correct reply to “Comment ...”. We consider a quantum chaotic macrosystem and demonstrate that no contradiction exists for this correct thermodynamical case. It must be mentioned that big size of a system (quantum or classic) is also not an enough condition for a system to be macroscopic. The macroscopic system must also be chaotic (quantum or classic) and has small chaotic interaction with its environment/observer resulting in decoherence (decorrelation). Indeed thermodynamic-like terminology is widely and effectively used in quantum mechanics, quantum computers field, and information theory. The big number of the examples is in the references of the authors’ paper. The other nice example is Shannon’s entropy in information theory. But usually such an author does not consider such a paper as analysis of classical Thermodynamics. Contrarily the authors (in “Comment ...”) “disprove” the second law of Thermodynamics on the basis of the irrelevant microscopic system and give the announcement of their next paper “Entanglement …” as a correct consideration and a disproof of the second law.
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