"In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities."
Statistical mechanics provides a theoretical framework for understanding the behavior of many-particle systems and is essential for understanding the thermodynamic properties of materials.
Probability theory: This is the foundation of statistical mechanics as it deals with the likelihood of an event occurring given certain conditions.
Boltzmann distribution: This distribution describes the statistical behavior of a system and how the energy is distributed among its components.
Microcanonical ensemble: This is a collection of microstates that are accessible to a physical system with a fixed energy, volume, and number of particles.
Canonical ensemble: This describes the behavior of a system that can exchange energy with its surroundings, but the number of particles and volume is fixed.
Grand canonical ensemble: This describes the behavior of a system that can exchange both energy and particles with its surroundings, but the volume is fixed.
Ensemble averages: The average value of a property of a system over all possible microstates in a given ensemble.
Partition function: This is a mathematical function that gives the probability distribution of the energy states of a system.
Density of states: This function gives the number of energy states of a system that are accessible to it.
Thermodynamics: The branch of science that deals with the relationship between heat, energy, and work.
Free energy: This is a thermodynamic quantity that measures the amount of work a system can do when it is in equilibrium with its surroundings.
Entropy: A measure of the disorder of a system.
Equilibrium: This refers to a state where the macroscopic variables of a system do not change with time.
Non-equilibrium: This refers to a state where the macroscopic variables of a system are changing with time.
Monte Carlo methods: A computational approach that uses random sampling to solve problems.
Molecular dynamics: A method that simulates the motion of particles in a system over time to study its behavior.
Phase transitions: The change in the physical properties of a system as it undergoes a change in its state.
Critical phenomena: The behavior of a system near a phase transition point.
Fluctuations: Random deviations of a system from its average behavior.
Correlation functions: Measures the strength of correlation between two quantities in a system.
Time correlation functions: These functions describe the time evolution of a system over time.
Monte Carlo simulation: Monte Carlo simulation is a statistical method used to model uncertainty in systems. It involves random sampling of a system which can be used to determine the overall behavior of a system.
Molecular Dynamics simulation: Molecular dynamics simulation is a method used to study the behavior of atoms and molecules. It involves solving the equations of motion for each atom and molecule in a system to determine how they interact and how the system evolves over time.
Ising Model: The Ising model is a mathematical model used to study the behavior of a certain class of physical systems. It is used to model ferromagnetism, and it can be used to study phase transitions in other systems as well.
Brownian Dynamics simulation: Brownian Dynamics simulation is a method used to study the behavior of particles in a fluid. It involves the simulation of the random motion of particles in a fluid due to collisions with the fluid molecules.
Density Functional Theory: Density Functional Theory is a computational method used to study the electronic structure of systems. It involves the solution of the Schrödinger equation to determine the energy and wave function of a system.
Kinetic Monte Carlo simulation: Kinetic Monte Carlo simulation is a method used to study the behavior of systems which are driven by kinetic processes such as diffusion or reaction. It involves the simulation of the stochastic nature of these processes to determine the overall behavior of the system.
Cellular Automata: Cellular Automata is a discrete model used to simulate the behavior of a system. It involves dividing a system into small cells and updating the state of each cell based on the states of its neighboring cells.
"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."