Decoherence, wave function collapses and non-ordinary statistical mechanics

Mauro Bologna, Paolo Grigolini, Marco G. Pala +1 more

Paolo Allegrini

We show that the derivation of Lévy statistics from a Liouville‐like approach is still an unresolved problem, even though a satisfactory derivation resting on the Generalized Central Limit Theorem (GCLT) has been obtained. We discuss a quantum relaxation that according to the supposed equivalence between decoherence theory and wave function collapses is expected to be equivalent to the characteristic function of a Lévy process. We notice that this way of proceeding is equivalent to establishing a finite Kolmogorov‐Sinai (KS) entropy, and consequently, a condition compatible with the Second Principle of Thermodynamics even though the connection between this kind of entropy and the Clausius entropy is not yet known. The quantum treatment, based on density rather than the collapse‐induced symbolic sequences, conflicts with this conclusion.

Roland L. Omnes

Phil Attard

The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum average. The mechanism for the collapse is found to be quite general: it results from the conservation law for a conserved, exchangeable variable (such as energy) and the entanglement of the total system wave function that necessarily follows. The relevance of the present results to the einselection mechanism for decoherence, to the quantum measurement problem, and to the classical nature of the macroscopic world are discussed.

Paolo Grigolini A

Bhushan Bhoja Poojary

We propose a novel hypothesis linking temperature to the frequency of wave function collapse in quantum systems. This framework connects thermodynamic entropy, quantum decoherence, and information theory, suggesting that higher temperatures correspond to increased wave function collapses due to enhanced environmental interactions. The mathematical models derived herein lay the foundation for experimental validation and bridge thermodynamics with quantum mechanics through a unified perspective. Keywords Thermodynamic entropy; Wave function; Quantum mechanics