Microstate (statistical mechanics)
Definition
A microstate in statistical mechanics is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. It is a complete description of the dynamical state of the system at the microscopic level.
Description
In statistical mechanics, a microstate is a specific arrangement of particles in a system. Each microstate is associated with a unique set of physical properties such as energy, pressure, and volume. The collection of all possible microstates for a system is known as the system's phase space.
Microstates and Macrostates
A macrostate, in contrast, is characterized by a set of macroscopic properties, and may correspond to many different microstates of the system. For example, if a gas is in thermal equilibrium, it can be described by macroscopic quantities like temperature and volume, but there are many arrangements of gas particles that could result in the same macroscopic state. Each of these arrangements is a different microstate.
Statistical Weight and Entropy
The statistical weight of a macrostate is the number of microstates that correspond to it. The concept of statistical weight is central to the definition of entropy in statistical mechanics. The entropy of a macrostate is a measure of the number of microstates corresponding to it. The more microstates a macrostate has, the higher its entropy.
Boltzmann's Entropy Formula
The relationship between entropy, statistical weight, and microstates is given by Boltzmann's entropy formula. This formula states that the entropy of a system is proportional to the logarithm of the number of microstates that correspond to a given macrostate. The constant of proportionality is Boltzmann's constant.
Microcanonical Ensemble
In the Microcanonical ensemble, all microstates are assumed to be equally probable. This is the simplest statistical ensemble, and it is used in the fundamental postulate of statistical mechanics, which states that for an isolated system in equilibrium, all accessible microstates are equally likely.
Canonical Ensemble
In the Canonical ensemble, the system is allowed to exchange energy with a heat bath at a fixed temperature. The probability of the system being in a particular microstate is then proportional to the Boltzmann factor, which is the exponential of the negative energy of the microstate divided by the product of Boltzmann's constant and the temperature of the heat bath.
Grand Canonical Ensemble
In the Grand canonical ensemble, the system is allowed to exchange both energy and particles with a reservoir. The probability of the system being in a particular microstate is given by the grand canonical distribution.
Quantum Statistical Mechanics
In quantum statistical mechanics, a microstate is a specific quantum state of the system. The concept of a microstate in quantum mechanics is similar to that in classical statistical mechanics, but with the additional feature of quantum superposition of states.