Overall homogeneity of temperature is a condition for thermal equilibrium, but, as is demonstrated by classical molecular dynamics simulations, the local temperatures of atoms in small, isolated crystalline clusters in microcanonical equilibrium are not uniform. The effective temperature determined from individual atomic velocity decreases with distance from the cluster center. It is argued that these effects are due to the conservation of angular and translational momentum. A general microcanonical expression is derived for the spatial dependence of the statistics of the kinetic energies of individual atoms; this fits the numerical observations well.
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http://dx.doi.org/10.1103/PhysRevLett.99.014102 | DOI Listing |
J Chem Phys
September 2024
Department of Chemical and Biomedical Engineering, Cleveland State University, Cleveland, Ohio 44115, USA.
A novel statistical mechanical methodology is applied to clusters of N ≤ 7 atoms. Exact statistical analogs for any energy derivative of entropy ∂mS/∂Em are used in rigorous microcanonical Monte Carlo simulations to vastly enlarge the pool of measurable thermodynamic properties relative to previous work. All analogs are given for two alternative partition functions of the microcanonical ensemble.
View Article and Find Full Text PDFSci Rep
March 2024
Pacific Northwest National Laboratory, Richland, WA, 99354, USA.
The hypergraph community detection problem seeks to identify groups of related vertices in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community labels and community-edge intersections. This algorithm can also be viewed as maximum-likelihood inference in a degree-corrected microcanonical stochastic blockmodel.
View Article and Find Full Text PDFJ Chem Theory Comput
December 2023
Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States.
Vibrational spectroscopy is widely used to gain insights into structural and dynamic properties of chemical, biological, and materials systems. Thus, an efficient and accurate method to simulate vibrational spectra is desired. In this paper, we justify and employ a microcanonical molecular simulation scheme to calculate the vibrational spectra of three challenging water clusters: the neutral water dimer (HO), the protonated water trimer (HO), and the protonated water tetramer (HO).
View Article and Find Full Text PDFJ Phys Chem A
October 2023
DTU Chemical Engineering, Technical University of Denmark, 2800 Lyngby, Denmark.
Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NHO potential energy surface, including the NH + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH oxidation with high sensitivity and high uncertainty.
View Article and Find Full Text PDFEntropy (Basel)
February 2023
Department of Chemical Engineering, Pennsylvania State University, State College, PA 16801, USA.
We study the set of integer partitions as a probability space that generates distributions and, in the asymptotic limit, obeys thermodynamics. We view ordered integer partition as a configuration of cluster masses and associate them with the distribution of masses it contains. We organized the set of ordered partitions into a table that forms a microcanonical ensemble and whose columns form a set of canonical ensembles.
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