Quantum Entropy

Davi Geiger, Zvi M. Kedem

Published 2021-06-29Version 1

All the laws of particle physics are time-reversible. A time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the second law of thermodynamics is introduced. In quantum physics, despite its intrinsically probabilistic nature, no mechanism for a time arrow has been proposed. We propose an entropy for quantum physics, which may conduce to the emergence of a time arrow. The proposed entropy is a measure of randomness over the degrees of freedom of a quantum state. It is dimensionless, it is a relativistic scalar, it is invariant under coordinate transformation of position and momentum that maintain conjugate properties, and under CPT transformations; and its minimum is positive due to the uncertainty principle.