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In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
A thermodynamic ensemble is a specific variety of statistical ensemble that, among other properties, is in statistical equilibrium (defined below), and is used to derive the properties of thermodynamic systems from the laws of classical or quantum mechanics. [3] [4]
Because of its connection with the elementary assumptions of equilibrium statistical mechanics (particularly the postulate of a priori equal probabilities), the microcanonical ensemble is an important conceptual building block in the theory. [2] It is sometimes considered to be the fundamental distribution of equilibrium statistical mechanics.
This dependence on microscopic variables is the central point of statistical mechanics. With a model of the microscopic constituents of a system, one can calculate the microstate energies, and thus the partition function, which will then allow us to calculate all the other thermodynamic properties of the system.
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
In statistical mechanics, the microcanonical ensemble is a particular statistical ensemble which is used to make predictions about the outcomes of experiments performed on isolated systems that are believed to be in equilibrium with an exactly known energy.
Statistical mechanics allows one to make insightful statements about the temporal behavior of such fluctuations of equilibrium systems. This is discussed below in the section on the temporal evolution of correlation functions and Onsager's regression hypothesis .
A fundamental assumption of statistical mechanics is that systems generically reach a state of thermal equilibrium (such as the Gibbs state) which can be characterized by only a few parameters such as temperature or a chemical potential. Traditionally, phase structure is studied by examining the behavior of ``order parameters" in equilibrium ...