"In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities."
A subfield that applies statistical methods to describe the behavior of large systems of particles.
Thermodynamics: The study of heat and its transformation to work.
Statistical ensembles: A collection of similar systems in different conditions.
Boltzmann distribution: A probability distribution used to determine the state of a system in thermal equilibrium.
Partition function: A function used to calculate the probabilities of the different states of a system.
Free energy: The energy that is available to do work.
Entropy: A measure of the disorder or randomness of a system.
Phase transitions: A change in the state of matter at a specific temperature and pressure.
Canonical ensemble: An ensemble of systems that are in thermal equilibrium with each other.
Grand canonical ensemble: An ensemble of systems that are in thermal and chemical equilibrium with each other.
Ising model: A model used to study the behavior of ferromagnetic materials.
Monte Carlo methods: A class of computational algorithms that rely on random sampling to obtain numerical results.
Molecular dynamics simulations: A method used to study the behavior of a system of interacting particles over time.
"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."