- Microstate (statistical mechanics)
In statistical mechanics, a microstate 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. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature and pressure.
A macrostate is characterized by a probability distribution of possible states across a certain statistical ensemble of all microstates. This distribution describes the probability of finding the system in a certain microstate. In the thermodynamic limit, the microstates visited by a macroscopic system during its fluctuations all have the same macroscopic properties.
Microscopic definitions of thermodynamic concepts
Statistical mechanics links the empirical thermodynamic properties of a system to the statistical distribution of an ensemble of microstates. All macroscopic thermodynamic properties of a system may be calculated from the partition function that sums the energy of all its microstates.
At any moment a system is distributed across an ensemble of N microstates, each denoted by i, and having a probability of occupation pi, and an energy Ei. These microstates form a discrete set as defined by quantum statistical mechanics, and Ei is an energy level of the system.
The internal energy is the mean of the system's energy
This is a microscopic statement of the first law of thermodynamics.
The absolute entropy exclusively depends on the probabilities of the microstates and is defined as
where kB is Boltzmann's constant.
Entropy is formulated by the second law of thermodynamics. The third law of thermodynamics is consistent with this definition, since zero entropy means that the macrostate of the system reduces to a single microstate.
Heat and work
Work is the energy transfer associated to the effect of an ordered, macroscopic action on the system. If this action acts very slowly then the Adiabatic theorem implies that this will not cause a jump in the energy level of the system. The internal energy of the system can only change due to a change of the energies of the system's energy levels.
The microscopic definitions of heat and work are the following:
The two above definitions of heat and work are among the few expressions of statistical mechanics where the sum corresponding to the quantum case cannot be converted into an integral in the classical limit of a microstate continuum. The reason is that classical microstates are usually not defined in relation to a precise associated quantum microstate, which means that when work changes the energy associated to the energy levels of the system, the energy of classical microstates doesn't follow this change.
- Quantum statistical mechanics
- Degrees of freedom (physics and chemistry)
- Ergodic hypothesis
- Phase space
Wikimedia Foundation. 2010.
Look at other dictionaries:
Statistical mechanics — is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.Statistical mechanics … Wikipedia
Partition function (statistical mechanics) — For other uses, see Partition function (disambiguation). Partition function describe the statistical properties of a system in thermodynamic equilibrium. It is a function of temperature and other parameters, such as the volume enclosing a gas.… … Wikipedia
Microstate continuum — A microstate continuum is the fluctuation spectrum of a thermodynamic system in the classical limit of high temperatures. Classical here is to be understood in opposition to quantum statistical mechanics. See also degrees of freedom (physics and… … Wikipedia
Microstate — The world s five smallest sovereign states: Vatican City, Monaco, Nauru, Tuvalu and San Marino, shown in the same scale for size comparison This article is about political geography. For the specific configuration of particles of a material in… … Wikipedia
Statistical thermodynamics — In thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory. Statistical thermodynamics, generally, provides a molecular level interpretation of thermodynamic… … Wikipedia
Statistical ensemble (mathematical physics) — In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1878, an ensemble (also statistical ensemble or thermodynamic ensemble)cite book |last=Kittel |first=Charles… … Wikipedia
Entropy (statistical thermodynamics) — In thermodynamics, statistical entropy is the modeling of the energetic function entropy using probability theory. The statistical entropy perspective was introduced in 1870 with the work of the Austrian physicist Ludwig Boltzmann. Mathematical… … Wikipedia
Second law of thermodynamics — The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at… … Wikipedia
Crooks fluctuation theorem — The Crooks equation (CE) is an equation in statistical mechanics that relates the work done on a system during a non equilibrium transformation to the free energy difference between the final and the initial state of the transformation. During … Wikipedia
Microcanonical ensemble — Statistical mechanics Thermodynamics · … Wikipedia