# Macrostate

In thermodynamics and statistical physics, a macrostate describes a system with many degrees of freedom (e.g. a gas that consists of 1 mol ~ individual particles), which is controlled by a few state variables such as energy , temperature , volume , pressure , chemical composition or magnetization is described. ${\ displaystyle 10 ^ {23}}$

In mechanics, a system can be particles fully describe by each particle to a location - and speed assigns vector. One speaks here of a microstate . This can be represented by a point in phase space . ${\ displaystyle N}$

For many particles ( number of particles ), however, it is practically impossible to determine an initial microscopic state or to solve the equation of motion for the system. In chaotic systems , the determination of the path of the system is also fundamentally impossible, since the smallest changes in the initial conditions lead to deviations of any size. ${\ displaystyle N \ sim 10 ^ {23}}$

However, the microscopic solution of the equation of motion is not even necessary, since the macroscopic properties only depend on a few parameters.

A very large number of micro-states are possible for a certain macrostate. These form a continuously distributed totality in the phase space. The macrostate is thus determined by a statistical concept ( probability distribution of the microstates). The fluctuations in the macroscopic sizes are negligibly small due to the high number of particles.

With macroscopic quantities one can establish macroscopic, deterministic laws. Do you know z. If, for example, the macroscopic state variables volume, temperature and number of particles for a gas, the pressure can be clearly calculated ( thermal equation of state of ideal gases ).