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Related Experiment Video

Updated: May 25, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism.

M Trovato¹, L Reggiani

¹Dipartimento di Matematica, Università di Catania, Viale A. Doria, I-95125 Catania, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 7, 2012

Summary

This study establishes the quantum maximum entropy principle as fundamental to quantum statistical mechanics. It develops a quantum hydrodynamic transport formalism, revealing nonlocal effects arise from density and temperature derivatives.

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Published on: December 4, 2017

Area of Science:

Quantum statistical mechanics
Quantum hydrodynamics
Theoretical physics

Background:

The principle of quantum maximum entropy is foundational for quantum statistical mechanics.
A comprehensive theoretical framework is needed for closed quantum hydrodynamic transport.

Purpose of the Study:

To develop a rigorous theoretical formalism for quantum hydrodynamic transport.
To investigate quantum contributions to transport phenomena using a Wigner function approach.
To establish the validity of the quantum maximum entropy principle in various conditions.

Main Methods:

Introduction of a quantum entropy functional for the reduced density matrix.
Development of a theoretical formalism for equilibrium and nonequilibrium conditions.
Expansion of Lagrange multipliers in powers of h(2) to derive quantum contributions.
Utilizing an arbitrary number of moments within the Wigner function approach.

Main Results:

Nonlocal effects on a macroscopic scale are linked to high-order spatial derivatives of numerical density and effective temperature.
Existing results for quantum Boltzmann gas and degenerate quantum Fermi gas are recovered.
Quantum Fermi and Bose gases statistics at different degeneracy levels are explicitly incorporated.
Exact analytical equations for relevant applications are provided.
The quantum maximum entropy principle is shown to be valid in the classical limit (h → 0).

Conclusions:

The developed formalism provides a rigorous method for studying quantum hydrodynamic transport.
The quantum maximum entropy principle offers a unified framework for diverse quantum gases.
The approach successfully bridges quantum and classical descriptions of transport phenomena.