Incoherence and negative entropy in the quantum 1/f effect of BAW and SAW quartz resonators

The application of the quantum 1/f theory to bulk acoustic wave (BAW) and surface acoustic wave (SAW) quartz resonators has so far been limited to the case of very high Q resonators in which the phonons are coherent throughout the resonator volume. Here the quantum 1/f theory is applied to the general case of an arbitrary coherence length of the phonons, which may be large or small compared with the size of the quartz resonator. This allows to extend the theory for the first time to low-and resonators in which the phonons are localized in a part of the resonator volume. The theory is also extended to include defect scattering along with the phonon scattering case exclusively published so far. The author´s recent application of the new Quantum Information Theory Approach (QIT, developed 1996) to Infra Quantum Physics (IQP) explains for the first time the apparent lack of unitarity caused by the entropy increase in the Quantum 1/f Effect (Q1/fE). Indeed, a more rigorous proof of the conventional Q2/fE is offered in this paper, which shows that actually there is pro resultant entropy increase and therefore unitarity is not violated. His new proof involves the concept of von Neumann Quantum Entropy, including the negative conditional entropy concept for quantum entangled states. The Q1/fE was applied to many high-tech systems, in particular to ultra-small electronic devices. The present paper explains how the additional entropy implied by the Q1/fE arises in spite of the entropy-conserving evolution of the system