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How to Partition a Quantum Observable.

Caleb Merrick Webb¹, Charles Allen Stafford¹

¹Department of Physics, University of Arizona, Tucson, AZ 85721, USA.

Entropy (Basel, Switzerland)

|July 26, 2024

Summary

This summary is machine-generated.

We introduce a Hilbert space partition for open quantum systems, defining an entropy current that governs local entropy fluctuations. This method ensures thermodynamic consistency, unlike other partitioning approaches.

Keywords:

entropy open quantum system partitioning thermodynamics

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Area of Science:

Quantum Mechanics
Statistical Mechanics
Thermodynamics

Background:

Open quantum systems exhibit complex dynamics influenced by their environment.
Understanding local entropy evolution is crucial for non-equilibrium statistical mechanics.
Existing formalisms may not consistently describe entropy partitioning.

Purpose of the Study:

To develop a consistent framework for partitioning quantum observables in open systems.
To analyze the local evolution of von Neumann entropy for independent quantum particles.
To investigate the relationship between entropy current and heat current under specific conditions.

Main Methods:

Partitioning of the Hilbert space or configuration space.
Derivation of an inhomogeneous continuity equation for observables.
Application to the local evolution of von Neumann entropy.
Analysis of system-reservoir coupling symmetry.

Main Results:

A partition of observables is inherited from Hilbert space division.
Local entropy fluctuations are governed by an entropy current operator.
Entropy current is equivalent to heat current for symmetrically coupled systems.
Asymmetric coupling partitions lead to entropy divergence.

Conclusions:

Hilbert-space partitioning provides a thermodynamically consistent framework for von Neumann entropy.
The derived entropy current operator governs local entropy changes.
This formalism clarifies the distinction between partitioned entropy and entanglement entropy production.