We derive the Boltzmann principle SB=kB ln W based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the 19th century in the works of Helmholtz and Boltzmann. Despite its simplicity, this argument has remained almost unknown. We present it in a contemporary, self-contained, and accessible form. The approach c...

As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with noncommutative algebra, such as NCAlgebra and NCComAlgebra, one simple method of calculating the commutator in quantum mechanics is put forward and is demonstrated...

Molecular dynamics (MD) based molecular mechanics Poisson-Boltzmann and surface area (MM-PB/SA) calculation (MD-PB/SA) has been widely used to estimate binding free energies for receptor-ligand complexes. While numerous reports have focused on assessing accuracy and efficiency, fewer studies have paid attention to performance in lead discovery. In the present study, we report a critical evaluat...

Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA), a method to estimate interaction free energies, has been increasingly used in the study of biomolecular interactions. Recently, this method has also been applied as a scoring function in computational drug design. Here a new tool g_mmpbsa, which implements the MM-PBSA approach using subroutines written in-house or sourced from the GR...

About 15 years ago, the steered molecular dynamics (SMD) was used to probe binding of ligand to biomolecule surfaces but in terms of drug design this approach has only recently attached attention of researchers. The main idea of using SMD to screen out leads is based on the hypothesis that the larger is the force needed to unbind a ligand from a receptor the higher its binding affinity. Thus, i...

" Design and implementation of a modern algebraic manipulator for Celestial Mechanics " , by Francesco Biscani ([email protected]), is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License Summary¹ e goals of this research are the design and implementation of a modern and efficient algebraic manipulator specialised for Celestial Mechanics. Specialised ...

This paper studies the Vlasov-Monge-Ampère system (VMA), a fully non-linear version of the Vlasov-Poisson system (V P ) where the (real) Monge-Ampère equation det ∂ Ψ ∂xi∂xj = ρ substitutes for the usual Poisson equation. This system can be derived as a geometric approximation of the Euler equations of incompressible fluid mechanics in the spirit of Arnold and Ebin. Global existence of weak sol...

Statistical mechanics is a branch of physics that applies probability theory, which contains mathematical tools for dealing with large populations, to the study of the thermodynamic behavior of systems composed of a large number of particles. A deep connection between probability theory and physics has been discovered in the research of statistical mechanics. The simplest model in statistical m...

We demonstrate that reciprocal Maupertuis’ Principle is the classical limit of Schrödinger’s Variational Principle in Quantum Mechanics. Misha Marinov loved analytical mechanics and understood its beauty. Canonical transformations, Poisson structures, symplectic geometry etc. were the notions that he constantly used in his original papers, and in his famous review on path integral. One of the a...

The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that this postulation is in fact unnecessary and may be replaced by a few deeper concepts, which ultimately lead to the derivation of Poisson bracket. One would onl...