Comparing classical and quantum PageRanks

Comparing classical and quantum equilibration.

By using a physically relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial state of the system is completely known (a pure state). This shows that quantum equilibration is a fundamental aspect of many quantum systems, while classical eq...

Cluster Enhanced Pageranks

On Classical, Fuzzy Classical, Quantum and Fuzzy Quantum Systems

In this paper we consider physical systems and the concept of their states in the context of the theory of fuzzy sets and systems. In section 1 we give a brief sketch on the fundamental difference between the theories of classical physics and quantum mechanics. In section 2 and 3 we introduce very shortly systems and their states in classical and quantum mechanics, respectively. Section 4 prese...

Between classical and quantum ∗

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of q...

Classical and Quantum Probability

We follow the development of probability theory from the beginning of the last century, emphasising that quantum theory is really a generalisation of this theory. The great achievements of probability theory, such as the theory of processes, generalised random fields, estimation theory and information geometry, are reviewed. Their quantum versions are then described.