The second law of thermodynamics for pure quantum states
Abstract
A version of the second law of thermodynamics states that one cannot lower the energy of an isolated system by a cyclic operation. We prove this law without introducing statistical ensembles and by resorting only to quantum mechanics. We choose the initial state as a pure quantum state whose energy is almost E_0 but not too sharply concentrated at energy eigenvalues. Then after an arbitrary unitary time evolution which follows a typical "waiting time", the probability of observing the energy lower than E_0 is proved to be negligibly small.
Keywords
Cite
@article{arxiv.1303.6393,
title = {The second law of thermodynamics for pure quantum states},
author = {Sheldon Goldstein and Takashi Hara and Hal Tasaki},
journal= {arXiv preprint arXiv:1303.6393},
year = {2013}
}
Comments
5 pages, endnotes [18], [20] are added for clarification in version 2. A major revision in version 3; the proof is drastically simplified, the discussion is extended, new references are added, and the two authors are added