Statistical mechanics begins as an effort to explain the macroscopic laws of thermodynamics by considering the microscopic application of Newton's laws to the particles that a material is made of.
Statistical mechanics averages properties of particles to find the properties of the material they form. For example, the temperature of a gas is found to be related to the random motion of the gas molecules. The faster they move on average, the higher the temperature. Heat transfer is the transfer of Newtonian energy of the particles of one object to the particles of the other object. In this way, the statistical treatment of the many particles of a material, with a key set of assumptions, reveals that thermodynamic laws are a natural consequence of many microscopic particles interacting with each other.
Since the study of complex systems is about understanding the relationship of the behavior of parts to the behavior of a system as a whole, many of the tools developed in statistical mechanics are useful in the study of complex systems.
Related concepts: thermodynamics, Newtonian mechanics, separation of scales, phase transitions.
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