![]() ![]() Nevertheless, the association of entropy with disorder is only colloquial, because in most cases we do not have quantitative descriptions of order. The link arises via probability, as the total number of arrangements is much larger than the number of arrangements that conform to a certain order principle. In that sense, loss of order is loss of information and increase of disorder is an increase in entropy. Finally, the paper considers the application of Von Neumann entropy in entanglement of formation for both pure and mixed bipartite quantum states. We can further associate order with information, as any ordered arrangement of objects contains information on how they are ordered. Both Shannon and Von Neumann entropy are discussed, making the connection to compressibility of a message stream and the generalization of compressibility in a quantum system. ![]() The equilibrium state is the macrostate that lacks most information on the underlying microstate. Lewis: "Gain in entropy always means loss of information, and nothing more". It follows, what was stated before Shannon by G. c The EE at h 0.3 < h c of von Neumann and 2nd Rényi obtained from DMRG with 72 × 12 cylinders and the QMC measurements on torus of size L × L with L 4, 6, 8, 10. The concept applies to non-equilibrium states as well as to equilibrium states. The more microstates are consistent with the observed macrostate, the larger is this number of questions and the larger are Shannon and Gibbs entropy. We note that this is exactly the type of experiment presumed in the second Penrose postulate (Section ). When expressed with the binary logarithm, this amount of Shannon information specifies the number of yes/no questions that would have to be answered to specify the microstate. In quantum information the logarithms are usually taken to be base 2, giving a maximum entropy of 1 for a qubit. ![]() It is the amount of Shannon information that is required to specify the microstate of the system if the macrostate is known. The von Neumann entropy of a quantum state is given by the formula, S () Tr (log) and if i are the eigenvalues of then the Von Neumann entropy can be reexpressed as: S () iilog (i). ![]()
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