In a more fundamental discussion thermodynamic equilibrium is described by a statistical
approach. This is true as well for all mechanisms leading to thermodynamic equilibrium, e.g. transport and scattering processes.
Brownian motion of tiny particles is a typical example for this.
This fundamental randomness can be
used in a famous mathematical concept to simulate transport phenomena, the ”path” to thermodynamic equilibrium,
and thermodynamic equilibrium properties of physical systems. To emphasize the statistical character this mathematical approach
is called ”Monte-Carlo-Simulation”. It is fundamentally a numerical approach on a computer. Each micro-state
within a thermodynamic system is defined by the set of values for each variable of each particle. The Monte-Carlo simulation
will modify successively the micro-state by ”testing” other values of these parameter. Random numbers generated
within a computer program can be used for three different purposes
Specifying the parameter which will be tested next.
Specifying a new value for this parameter.
Accept the parameter change with a certain probability depending on the energy change related to the value change.
With nowadays increasing computer power (Monte-Carlo-)simulation become even more popular and relevant. Many different versions of Monte-Carlo-simulation exist optimizing efficiency, stability, and accuracy of the algorithms. Here we only will discuss briefly one of the oldest but due to it’s simplicity still very important algorithms.
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© J. Carstensen (Comp. Math.)