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Free Energy and Entropy Changes: From Molecular Dynamics Simulations to the Developing Theories of Small Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Non-equilibrium Phenomena".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 8130

Special Issue Editors


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Guest Editor
Department of Engineering, University of Campania "L. Vanvitelli", Aversa (CE), Italy
Interests: non-equilibrium statistical mechanics; fluctuation-dissipation relations; granular systems; anomalous diffusion
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Guest Editor
School of Natural Sciences, Griffith University, Brisbane, QLD 4111, Australia
Interests: computational physics; biophysics; fluid; molecular dynamics; thermodynamics; mathematical modelling; finite element method; applied mathematics

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Guest Editor
Department of Physics and Biophysics, Faculty of Food Science, University of Warmia and Mazury in Olsztyn, Oczapowskiego 4, 10-719 Olsztyn, Poland
Interests: coarse-grained models; molecular dynamics; quantum chemistry; machine learning
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Special Issue Information

Dear Colleagues

Non-equilibrium systems, natural, biological or man-made, pose new challenges to the development of a general theory, capable of predicting the main macroscopic behaviors from the microscopic dynamics. Nevertheless, recently, important general results have been obtained, pushing the range of applicability of concepts of standard thermodynamics into the realm of out-of-equilibrium phenomena.

For instance, one of the central problems in molecular biology is the estimation of the affinity of macromolecules forming macromolecular complexes as well as affinities of small molecules (possible inhibitors) towards macromolecules (proteins or nucleic acids). The latter process is especially important because of its possible practical applications in the drug design process. These mechanisms depend on a delicate balance between enthalpy change, which usually favors the association process, and entropy change, which usually opposes the complexation. Estimation of configurational entropy change of solute and solvent is therefore a particularly challenging and important task.

On the theoretical side, one of the most relevant results in the theory of non-equilibrium systems is the Jarzynski equality, relating the statistics of the exponential of the mechanical work done by external agents and the free energy difference between initial and final equilibrium states. Although the derivations of the Jarzynski equality seem to be quite general, the definitions of the quantities appearing in it, the work in particular, and the interpretation of certain experiments are still at the core of an intense debate.  As a matter of fact, the Jarzynski equality falls within the set of theories meant to describe small, strongly coupled, and long ranged interacting systems. This is a wide open although long-established field, of particular interest in nanotechnology, and well beyond.

This Special Issue serves as a platform for presentation of results in the wide context of non-equilibrium systems, with specific focus on new and improved techniques developed for estimation of free energy changes in macromolecular systems, or more in general on the study of the fluctuations of thermodynamics quantities such as heat, work or entropy production in different systems.  Original research papers, reviews/perspectives and short communications covering theory and applications are welcome.

Dr. Alessandro Sarracino
Prof. Dr. Owen Jepps
Dr. Maciej Maciejczyk
Guest Editors

 

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • ensembles
  • free energy
  • work
  • mesoscopic systems
  • foundations
  • protein stretching
  • stochastic thermodynamics
  • absolute irreversibility
  • virial
  • non-equilibrium

Published Papers (4 papers)

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Research

14 pages, 3069 KiB  
Article
Work and Thermal Fluctuations in Crystal Indentation under Deterministic and Stochastic Thermostats: The Role of System–Bath Coupling
by Javier Varillas and Lamberto Rondoni
Entropy 2022, 24(9), 1309; https://0-doi-org.brum.beds.ac.uk/10.3390/e24091309 - 15 Sep 2022
Viewed by 1256
Abstract
The Jarzynski equality (JE) was originally derived under the deterministic Hamiltonian formalism, and later, it was demonstrated that stochastic Langevin dynamics also lead to the JE. However, the JE has been verified mainly in small, low-dimensional systems described by Langevin dynamics. Although the [...] Read more.
The Jarzynski equality (JE) was originally derived under the deterministic Hamiltonian formalism, and later, it was demonstrated that stochastic Langevin dynamics also lead to the JE. However, the JE has been verified mainly in small, low-dimensional systems described by Langevin dynamics. Although the two theoretical derivations apparently lead to the same expression, we illustrate that they describe fundamentally different experimental conditions. While the Hamiltonian framework assumes that the thermal bath producing the initial canonical equilibrium switches off for the duration of the work process, the Langevin bath effectively acts on the system. Moreover, the former considers an environment with which the system may interact, whereas the latter does not. In this study, we investigate the effect of the bath on the measurable quantity of the JE through molecular dynamics simulations of crystal nanoindentation employing deterministic and stochastic thermostats. Our analysis shows that the distributions of the kinetic energy and the mechanical work produced during the indentation processes are affected by the interaction between the system and the thermostat baths. As a result, the type of thermostatting has also a clear effect on the left-hand side of the JE, which enables the estimation of the free-energy difference characterizing the process. Full article
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10 pages, 2405 KiB  
Article
Stochastic Thermodynamics of an Electromagnetic Energy Harvester
by Luigi Costanzo, Alessandro Lo Schiavo, Alessandro Sarracino and Massimo Vitelli
Entropy 2022, 24(9), 1222; https://0-doi-org.brum.beds.ac.uk/10.3390/e24091222 - 31 Aug 2022
Cited by 7 | Viewed by 1667
Abstract
We study the power extracted by an electromagnetic energy harvester driven by broadband vibrations. We describe the system with a linear model, featuring an underdamped stochastic differential equation for an effective mass in a harmonic potential, coupled electromechanically with the current in the [...] Read more.
We study the power extracted by an electromagnetic energy harvester driven by broadband vibrations. We describe the system with a linear model, featuring an underdamped stochastic differential equation for an effective mass in a harmonic potential, coupled electromechanically with the current in the circuit. We compare the characteristic curve (power vs. load resistance) obtained in experiments for several values of the vibration amplitude with the analytical results computed from the model. Then, we focus on a more refined analysis, taking into account the temporal correlations of the current signal and the fluctuations of the extracted power over finite times. We find a very good agreement between the analytical predictions and the experimental data, showing that the linear model with effective parameters can describe the real system, even at the fine level of fluctuations. Our results could be useful in the framework of stochastic thermodynamics applied to energy harvesting systems. Full article
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14 pages, 1038 KiB  
Article
Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems
by Jaime Aspas-Caceres, Marc Rico-Pasto, Isabel Pastor and Felix Ritort
Entropy 2022, 24(7), 895; https://0-doi-org.brum.beds.ac.uk/10.3390/e24070895 - 29 Jun 2022
Viewed by 1512
Abstract
Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks [...] Read more.
Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime. Full article
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12 pages, 2145 KiB  
Article
Stochastic Thermodynamics of a Piezoelectric Energy Harvester Model
by Luigi Costanzo, Alessandro Lo Schiavo, Alessandro Sarracino and Massimo Vitelli
Entropy 2021, 23(6), 677; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060677 - 27 May 2021
Cited by 10 | Viewed by 2606
Abstract
We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a capacitor and a load resistor, can accurately describe [...] Read more.
We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a capacitor and a load resistor, can accurately describe the experimental data. In particular, the theoretical model allows us to define fluctuating currents and to study the stochastic thermodynamics of the system, with focus on the distribution of the extracted work over different time intervals. Our analytical and numerical analysis of the linear model is succesfully compared to the experiments. Full article
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