"In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities."
The study of the behavior of large systems using statistical methods.
Probability Theory: Probability theory is the study of random phenomena and provides a theoretical framework for the analysis of statistical data. It is a fundamental concept in statistical mechanics.
Thermodynamics: Thermodynamics is the branch of physics that studies the relationships between heat, work, energy, and temperature. It is an important concept in statistical mechanics, as it relates to the behavior of large numbers of particles.
Statistical Ensembles: Statistical ensembles are collections of systems that share the same macroscopic properties, but differ in their microscopic details. They are useful for modeling the behavior of large numbers of particles.
Phase Transitions: Phase transitions are changes in the physical properties of a system when it undergoes a change in temperature, pressure, or other external parameters. They are important in statistical mechanics because they can be used to model the behavior of complex systems.
Quantum Mechanics: Quantum mechanics is the branch of physics that studies the behavior of matter and energy at the microscopic level. It is important in statistical mechanics because it provides a framework for understanding the behavior of individual particles.
Entropy: Entropy is a measure of the disorder or randomness in a system. It is a fundamental concept in statistical mechanics because it can be used to predict the behavior of large numbers of particles.
Partition Functions: Partition functions are mathematical functions that describe the statistical properties of a system. They are used to predict the behavior of large numbers of particles.
Ideal Gases: Ideal gases are theoretical gases that have certain properties that make them easier to study. They are important in statistical mechanics because they provide a simple model for calculating the behavior of large numbers of particles.
Kinetic Theory of Gases: The kinetic theory of gases is a theory that explains the behavior of gases in terms of the motion of individual particles. It is important in statistical mechanics because it provides a framework for understanding the behavior of large numbers of particles.
Brownian Motion: Brownian motion is the random motion of particles suspended in a fluid. It is important in statistical mechanics because it provides a model for the behavior of large numbers of particles.
Fluctuation-Dissipation Theorem: The fluctuation-dissipation theorem is a fundamental concept in statistical mechanics that links the fluctuations in a system to the dissipation of energy.
Monte Carlo Methods: Monte Carlo methods are computer simulation techniques that are used to model the behavior of complex systems. They are important in statistical mechanics because they provide a way to study the behavior of large numbers of particles.
Equilibrium statistical mechanics: The study of physical systems in which the particles are at equilibrium with their surroundings, meaning that the energy distribution of the particles does not change over time.
Non-equilibrium statistical mechanics: The study of physical systems that are not at equilibrium, and may exhibit a variety of non-equilibrium behaviors and statistical properties.
Quantum statistical mechanics: The application of statistical mechanics to systems where quantum mechanics is the dominant physics, as opposed to classical mechanics.
Classical statistical mechanics: The application of statistical mechanics to systems where classical mechanics is the dominant physics, as opposed to quantum mechanics.
Stochastic statistical mechanics: The application of statistical mechanics to systems with stochastic or random behavior, such as diffusion.
Dynamic statistical mechanics: The study of the evolution of statistical systems over time, including the behavior of particles and groups of particles as they interact.
Thermodynamic statistical mechanics: The application of statistical mechanics to thermodynamic systems, such as gases and solids.
Statistical field theory: The application of statistical mechanics to systems where the fundamental objects are not particles, but rather fields, such as in the study of quantum electrodynamics.
Numerical statistical mechanics: The use of numerical simulations to study statistical mechanics, using techniques such as Monte Carlo simulations.
Topological statistical mechanics: The study of topological properties of statistical systems, such as the behavior of particles on surfaces or in different geometries.
Mesoscopic statistical mechanics: The study of the behavior of statistical systems at the mesoscopic scale, where the system is too large to be studied as an individual particle or atom, but too small to be treated as a macroscopic system.
Information-theoretic statistical mechanics: The study of the relationship between information and statistical mechanics, including the use of entropy measures to study complex systems.
"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."