PhilSci Archive

When do Gibbsian Phase Averages and Boltzmannian Equilibrium Values Agree?

Werndl, Charlotte and Frigg, Roman (2020) When do Gibbsian Phase Averages and Boltzmannian Equilibrium Values Agree? [Preprint]

[img]
Preview
Text
ManuscriptFinal.pdf

Download (595kB) | Preview

Abstract

This paper aims to shed light on the relation between Boltzmannian statistical mechanics and Gibbsian statistical mechanics by studying the Mechanical Averaging Principle, which says that, under certain conditions, Boltzmannian equilibrium values and Gibbsian phase averages are approximately equal. What are these conditions? We identify three conditions each of which is individually sufficient (but not necessary) for Boltzmannian equilibrium values to be approximately equal to Gibbsian phase averages: the Khinchin condition, and two conditions that result from two new theorems, the Average Equivalence Theorem and the Cancelling Out
Theorem. These conditions are not trivially satisfied, and there are core models of statistical mechanics, the six-vertex model and the Ising model, in which they fail.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Werndl, Charlotte
Frigg, Roman
Keywords: statistical mechanics, Boltzmann, Gibbs, phase averages, equilibrium, Ising model, six-vertex model
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Charlotte Werndl
Date Deposited: 21 Sep 2021 03:06
Last Modified: 21 Sep 2021 03:06
Item ID: 19600
Official URL: https://www.sciencedirect.com/science/article/pii/...
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: 2020
URI: http://philsci-archive.pitt.edu/id/eprint/19600

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item