"In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities."
Branch of physics that studies the behavior of large numbers of particles, including molecules.
Probability theory: An understanding of basic probability theory is needed to build a foundation for statistical mechanics.
Statistical Ensembles: Statistical ensembles define the boundaries within which statistical mechanics is applied in physics and chemistry.
Thermodynamics: Thermodynamic concepts are required to understand the behavior of systems at a macroscopic level.
Quantum Mechanics: The principles of quantum mechanics are applied in molecular systems, and it integrates with the statistical mechanics approach.
Molecular Dynamics Simulation: Molecular dynamics simulations are used to investigate the movement of atoms and molecules.
Monte Carlo Simulation: Monte Carlo simulations are used to generate random states of a system according to a statistical ensemble.
Free Energy Calculations: Free energy calculations are a central tool for understanding the thermodynamics of molecular systems and for predicting reaction rates.
Monte Carlo Methods for Free Energy Calculations: Monte Carlo methods are used for free energy calculations, as they offer a flexible framework for generating and analyzing statistical ensembles.
Molecular Modeling: Molecular modeling is the process of creating three-dimensional structures and visualizing molecular systems, which is vital in computational chemistry.
Molecular Energy Landscapes: This topic is about the energy landscapes of molecules, and it includes the concept of energetic barriers and transition states.
Entropy: Entropy is an essential thermodynamic quantity that describes how a system disperses its energy into disorder.
Molecular Mechanics: Molecular mechanics is the mathematical representation of molecular mechanical movement and relies on energy potential functions.
Statistical Mechanics of Liquids: This topic is concerned with understanding the thermodynamics and kinetics of liquids, which are essential in biological and chemical systems.
Phase Transitions: Phase transitions are transitions from one state of matter to another and occur due to the fluctuations in energy and entropy.
Polymer Science: Statistical mechanics is applied in the study of polymers to explain its properties, structure, and behavior.
Diffusion: The movement of particles in a system is referred to as diffusion, which is often used to calculate reaction rates and transport properties.
Kinetic Theory of Gases: The kinetic theory of gases offers a connection between the macroscopic properties of gases, such as pressure and volume, and the behavior of individual gas molecules.
Brownian Motion: Brownian motion describes the random movement of particles suspended in liquids or gases due to collisions with the surrounding molecules.
Statistical Mechanics of Biological Systems: This topic applies statistical techniques to biological systems, such as modeling protein folding and misfolding.
Computational Methods: Computational methods, such as Density Functional Theory (DFT), Quantum Monte Carlo (QMC), and Coupled Cluster (CC) methods, are mathematical tools that use chemical and physical principles to model molecular systems.
Non-Equilibrium Statistical Mechanics: Non-equilibrium statistical mechanics deals with the behavior of systems that are not at equilibrium, for example, those in biological processes where there is no steady-state.
Dynamic Simulation: Dynamic simulations describe the behavior of molecules over time using algorithms that solve the equations that govern their movement.
Electron Correlation: Electron correlation deals with the interactions between electrons and how they affect the physical and chemical properties of molecules.
Molecular Recognition: Molecular recognition describes how molecules interact or recognize each other through specific molecular interactions, such as hydrogen bonds or Van der Waals forces.
Chemical Kinetics: Chemical Kinetics is the study of the rates of chemical reactions.
Transport Properties: Transport properties refer to the diffusion of particles in a fluid or gas.
Biomolecular Dynamics: The study of the dynamics of biomolecules, which are essential in understanding biological processes like enzymes and drug-receptor interactions.
Statistical Physics in Materials Science: This topic applies statistical mechanics concepts to the study of materials science, such as crystal structure prediction or understanding the behavior of glasses.
Free Energy Sampling Techniques: Techniques for free energy calculation through enhanced sampling, the umbrella sampling method, and many other weight functions.
Reaction Mechanisms and Pathways: Understanding multistep reactions, potential energy surfaces, and catalytic activity through statistical statistical methods.
Canonical Ensemble: It is a type of Statistical Mechanics that models the equilibrium between a system and its surroundings, at constant temperature, volume, and number of particles.
Grand Canonical Ensemble: It is another type of Statistical Mechanics that models open systems where particles can exchange both energy and particles with its reservoir.
Microcanonical Ensemble: It is a type of Statistical Mechanics that models an isolated system that contains a constant amount of energy.
Isobaric-Isenthalpic Ensemble: It is a type of Statistical Mechanics that models systems at fixed pressure and enthalpy.
Replica Exchange Monte Carlo (REMC): It is a type of Statistical Mechanics that combines Monte Carlo simulation and molecular dynamics simulation to accelerate the search for low-energy states in systems with rugged energy landscapes.
Transition State Sampling (TSS): It is a type of Statistical Mechanics that models chemical reactions by sampling the transition states that connect reactant and product states.
Kinetic Monte Carlo (KMC): It is a type of Statistical Mechanics that models the dynamics of chemical systems by simulating the trajectory of individual particles based on their chemical reactions and interactions.
Density Functional Theory (DFT): It is a type of Statistical Mechanics that calculates the electronic structure of molecules based on the density of their electron clouds.
Ab Initio Molecular Dynamics (AIMD): It is a type of Statistical Mechanics that models the dynamics of chemical systems by solving the Schrodinger equation for all the particles in the system.
Coarse-Grained Models: It is a type of Statistical Mechanics that models complex systems by reducing their level of detail and treating them as a collection of interacting particles or units.
"It explains the macroscopic behavior of nature from the behavior of such ensembles."
"Its applications include many problems in the fields of physics, biology, chemistry, and neuroscience."
"Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion."
"Statistical mechanics arose out of the development of classical thermodynamics."
"Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates."
"James Clerk Maxwell, who developed models of probability distribution of such states."
"Josiah Willard Gibbs, who coined the name of the field in 1884."
"Non-equilibrium statistical mechanics focuses on the issues of microscopically modeling the speed of irreversible processes that are driven by imbalances."
"Examples of such processes include chemical reactions and flows of particles and heat."
"The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles."
"It applies statistical methods and probability theory."
"It does not assume or postulate any natural laws."
"It explains the macroscopic behavior of nature from the behavior of such ensembles."
"Classical thermodynamics is primarily concerned with thermodynamic equilibrium."
"Microscopic parameters fluctuate about average values and are characterized by probability distributions."
"It clarifies the properties of matter in aggregate, in terms of physical laws governing atomic motion."
"Physics, biology, chemistry, and neuroscience."
"Microscopically modeling the speed of irreversible processes that are driven by imbalances."
"Ludwig Boltzmann, James Clerk Maxwell, and Josiah Willard Gibbs."