scholarly journals A phase space sampling approach to equilibrium semiclassical statistical mechanics

1977 ◽  
Vol 67 (12) ◽  
pp. 5894-5903 ◽  
Author(s):  
Richard M. Stratt ◽  
William H. Miller
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Approach To Equilibrium ◽  
Sampling Approach

scholarly journals Themis: A Software to Assess Association Free Energies via Direct Estimative of Partition Functions

2020 ◽  
Author(s):  
Felippe Mariano Colombari ◽  
Asdrubal Lozada-Blanco ◽  
Kalil Bernardino ◽  
Weverson Gomes ◽  
André Farias de Moura
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Excited States ◽  
Surface Adsorption ◽  
Chiral Discrimination ◽  
Partition Functions ◽  
Computer Implementation ◽  
Free Energies ◽  
Electronic Excited States ◽  
Discrete Grid

<div>We present the program <i>Themis</i> - a computer implementation of a standard statistical mechanics framework to compute free energies, average energies and entropic contributions for association processes of two atom-based structures. The partition functions are computed analytically using a discrete grid in the phase space, whose size and degree of coarseness can be controlled to allow efficient calculations and to achieve the desired level of accuracy. With this strategy, applications ranging from molecular recognition, chiral discrimination, surface adsorption and even the interactions involving molecules in electronic excited states can be handled.</div>

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

Phase-space dynamics and ergodicity

2021 ◽  
pp. 79-98
Author(s):  
James P. Sethna
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Dissipative Systems ◽  
Planetary Motion ◽  
Equilibrium Statistical Mechanics ◽  
Average Behavior ◽  
Time Average ◽  
Space Dynamics ◽  
Mathematical Justification ◽  
Liouville’S Theorem

This chapter provides the mathematical justification for the theory of equilibrium statistical mechanics. A Hamiltonian system which is ergodic is shown to have time-average behavior equal to the average behavior in the energy shell. Liouville’s theorem is used to justify the use of phase-space volume in taking this average. Exercises explore the breakdown of ergodicity in planetary motion and in dissipative systems, the application of Liouville’s theorem by Crooks and Jarzynski to non-equilibrium statistical mechanics, and generalizations of statistical mechanics to chaotic systems and to two-dimensional turbulence and Jupiter’s great red spot.

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