"In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities."
The study of how the behavior of macroscopic systems can be explained through the behavior of individual particles.
Probability theory: The mathematical framework for understanding the likelihood of events occurring in a system.
Thermodynamics: The study of the relationships between heat, work, and energy in a system.
Kinetic theory of gases: The use of statistical mechanics to describe the behavior of gases and their properties.
Partition functions: A mathematical tool used to determine the thermodynamic properties of a system.
Boltzmann distribution: The relationship between the energy of a system and its probability of being in a particular state.
Ensemble theory: The study of the statistical properties of large groups of particles or systems.
Quantum mechanics: The fundamental theory used to understand the behavior of particles at the atomic and subatomic level.
Molecular dynamics simulations: The use of computational methods to simulate the behavior of molecules and their interactions with their environment.
Phase transitions: The changes in the physical properties of a system as it undergoes a change in its thermodynamic state.
Monte Carlo simulations: A computational method used to simulate the behavior of a system by randomly sampling from a probability distribution.
Classical statistical mechanics: This branch of statistical mechanics deals with macroscopic systems that can be described by classical mechanics. It is mainly used to study equilibrium properties of gases, liquids, solids, and other non-quantum mechanical systems.
Quantum statistical mechanics: This branch of statistical mechanics is used to describe the behavior of quantum mechanical systems at equilibrium. It is used to study the behavior of systems of particles that are interacting with one another via quantum mechanical forces.
Non-equilibrium statistical mechanics: This branch of statistical mechanics is used to study the behavior of systems that are not in thermodynamic equilibrium. It is used to study the behavior of systems that are evolving over time (e.g., chemical reactions, biological systems, etc.).
Molecular dynamics: This type of statistical mechanics uses computer simulation to study the behavior of atoms and molecules in systems that are in thermodynamic equilibrium. It involves modeling the motion of the particles in the system based on classical mechanics.
Monte Carlo simulations: This type of statistical mechanics also uses computer simulation to study systems in thermodynamic equilibrium. It involves generating random configurations of the system and calculating the thermodynamic properties of the system based on these configurations.
Density functional theory: This type of statistical mechanics is used to study the electronic structure of systems. It involves using a functional of the electronic density to determine the energy of the system.
"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."