# Representative Ensembles in Statistical Mechanics

## TL;DR

This paper rigorously formulates the concept of representative ensembles in statistical mechanics, demonstrating their importance for consistent and accurate descriptions of systems like Bose condensates, ensuring conservation laws and gapless spectra.

## Contribution

It introduces a strict formulation of representative ensembles, ensuring consistent and physically accurate descriptions of statistical systems such as Bose-condensed systems.

## Key findings

- A self-consistent treatment with representative ensembles yields a conserving theory.
- The approach guarantees a gapless spectrum in Bose-condensed systems.
- Proper ensemble choice avoids theoretical inconsistencies.

## Abstract

The notion of representative statistical ensembles, correctly representing statistical systems, is strictly formulated. This notion allows for a proper description of statistical systems, avoiding inconsistencies in theory. As an illustration, a Bose-condensed system is considered. It is shown that a self-consistent treatment of the latter, using a representative ensemble, always yields a conserving and gapless theory.