Regular system

Graduated

In statistics, shaped (English: Ensemble ) represents a large number of possible conditions under certain conditions A collection of states. That is, the system is a probability distribution of the system state. For a system of the same properties, its microscopic state (such as the position and speed of each particles) can still be substantially different. (In fact, for a macro system, all possible numbers are astronomical numbers.) In the literature of probability and mathematical statistics, use "probability space" to refer to the same concept.

A principle of statistical physics (all state passwords) is: For a balanced system, the amount of physical quantity is average, equal to the average result of all systems that are engraved in the corresponding system. The physical properties of the equilibrium state of the

system can be obtained for different microscopic states. The concept is made by Jessia Gibbs in 1878.

Common systems:

• microCanonical Ensemble): Each system of cross-miles (usually each The number of particles and volume of the system is also the same).

• CANONICAL ENSEMBLE: Comprehensive system can exchange energy with other systems (number of particles and volume of each system are still fixed and the same) However, all systems in the system have the same temperature.

• Giant Ensembles: The promotion of regular system, each system can exchange energy and particles with other systems, but all systems in the system have the same Temperature and chemical potential.

• Isothermal-IsoBaric Ensemble: The promotion of regular system, each system can exchange energy and volume with other systems, but all systems in the system have The same temperature and pressure.

In the system, the ratio of the physical quantity and its own size is reduced as the system becomes large. Thus, for a macro system, the difference in physical quantity calculated from various series will tend to zero.

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Regular system ( canonical Ensemble ) is a comprehensive system in statistics. It represents a collection of systems with the same temperature. The regular system is the most common application.

The number of particles and volumes of each system in the form of synthetic systems are fixed. However, each system can exchange energy with other systems in the system. At the same time, the total energy of all systems, and the number of systems are fixed. Under these conditions, when all systems are allocated to different micro-states, we found that the number of systems in each micro-state is proportional to

. Where

,

is Bolzman constant,

is an absolute temperature.

Regular series of bibliographic functions,

, is:

The logarithm of the distribution function is Helmhoz free energy (Helmholtz Free Energy, Symbol

)

After the division function calculates, the average energy can directly from

The first-order derivative is obtained.

Reference

• statistics

• Micro-regular system

• 正 则 系

• isothermal iszide system