Quantum Entropy

TL;DR

This paper introduces a new quantum entropy measure based on conjugate observables, which quantifies the randomness of quantum states and obeys an entropy law suggesting a time arrow in particle physics.

Contribution

It proposes a novel quantum entropy that is invariant, positive, and extends to mixed states, differing from von Neumann entropy and implying a fundamental entropy law.

Findings

The entropy is dimensionless and relativistic.

It is always larger than von Neumann's entropy.

The entropy law suggests entropy of closed systems never decreases.

Abstract

Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair of observables forming the quantum phase space. The entropy 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. We expand the entropy to also include mixed states and show that the proposed entropy is always larger than von Neumann's entropy. We conjecture an entropy law whereby that entropy of a closed system never decreases, implying a time arrow for particles physics.