Next Article in Journal
Wax-Printed Fluidic Time Delays for Automating Multi-Step Assays in Paper-Based Microfluidic Devices (MicroPADs)
Next Article in Special Issue
A Thermodynamic Model for Lithium-Ion Battery Degradation: Application of the Degradation-Entropy Generation Theorem
Previous Article in Journal
Analysis of an H∞ Robust Control for a Three-Phase Voltage Source Inverter
Previous Article in Special Issue
Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 2: Two-Phase Ejectors
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle
Inventions 2019, 4(1), 19; https://doi.org/10.3390/inventions4010019

Full Statistics of Conjugated Thermodynamic Ensembles in Chains of Bistable Units

1
Institute of Electronics, Microelectronics and Nanotechnology CNRS-UMR 8520, Univ. Lille, Centrale Lille, ISEN, Univ. Valenciennes, LIA LICS/LEMAC, F-59000 Lille, France
2
Laboratoire de Physique Statistique, Ecole Normale Supérieure, CNRS-UMR 8550, 75005 Paris, France
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 7 January 2019 / Revised: 8 March 2019 / Accepted: 9 March 2019 / Published: 14 March 2019
(This article belongs to the Special Issue Thermodynamics in the 21st Century)
  |  
PDF [1516 KB, uploaded 14 March 2019]
  |  

Abstract

The statistical mechanics and the thermodynamics of small systems are characterized by the non-equivalence of the statistical ensembles. When concerning a polymer chain or an arbitrary chain of independent units, this concept leads to different force-extension responses for the isotensional (Gibbs) and the isometric (Helmholtz) thermodynamic ensembles for a limited number of units (far from the thermodynamic limit). While the average force-extension response has been largely investigated in both Gibbs and Helmholtz ensembles, the full statistical characterization of this thermo-mechanical behavior has not been approached by evaluating the corresponding probability densities. Therefore, we elaborate in this paper a technique for obtaining the probability density of the extension when force is applied (Gibbs ensemble) and the probability density of the force when the extension is prescribed (Helmholtz ensemble). This methodology, here developed at thermodynamic equilibrium, is applied to a specific chain composed of units characterized by a bistable potential energy, which is able to mimic the folding and unfolding of several macromolecules of biological origin. View Full-Text
Keywords: small systems thermodynamics; Gibbs and Helmholtz ensembles; polymer chain; bistability; ensembles equivalence small systems thermodynamics; Gibbs and Helmholtz ensembles; polymer chain; bistability; ensembles equivalence
Figures

Graphical abstract

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

Benedito, M.; Manca, F.; Giordano, S. Full Statistics of Conjugated Thermodynamic Ensembles in Chains of Bistable Units. Inventions 2019, 4, 19.

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.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Inventions EISSN 2411-5134 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top