Next Article in Journal
Entropic Phase Maps in Discrete Quantum Gravity
Next Article in Special Issue
Quality Systems. A Thermodynamics-Related Interpretive Model
Previous Article in Journal
Regularizing Neural Networks via Retaining Confident Connections
Article Menu
Issue 7 (July) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(7), 314; https://doi.org/10.3390/e19070314

Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law

1
Instítuto de Física, Universidad Nacional Autónoma de México, Mexico City 01000, Mexico
2
Unidad Multidisciplinaria de Docencia e Investigación-Facultad de Ciencias, Universidad Nacional Autónoma de México, Campus Juriquilla, Queretaro 76230, Mexico
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 18 May 2017 / Revised: 21 June 2017 / Accepted: 24 June 2017 / Published: 30 June 2017
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
Full-Text   |   PDF [327 KB, uploaded 30 June 2017]   |  

Abstract

It is often incorrectly assumed that the number of microstates Ω ( E , V , N , . . . ) available to an isolated system can have arbitrary dependence on the extensive variables E , V , N , ... However, this is not the case for systems which can, in principle, reach thermodynamic equilibrium since restrictions arise from the underlying equilibrium statistical mechanic axioms of independence and a priori equal probability of microstates. Here we derive a concise criterion specifying the condition on Ω which must be met in order for a system to be able, in principle, to reach thermodynamic equilibrium. Natural quantum systems obey this criterion and therefore can, in principle, reach thermodynamic equilibrium. However, models which do not respect this criterion will present inconsistencies when treated under equilibrium thermodynamic formalism. This has relevance to a number of recent models in which negative heat capacity and other violations of fundamental thermodynamic law have been reported. View Full-Text
Keywords: modeling small systems; microstate densities; thermodynamics of small systems; negative heat capacity; violation of thermodynamic law; ergodicity modeling small systems; microstate densities; thermodynamics of small systems; negative heat capacity; violation of thermodynamic law; ergodicity
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Michaelian, K.; Santamaría-Holek, I. Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law. Entropy 2017, 19, 314.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top