## The Statistical Interpretation of Entropy

A more physical interpretation of entropy had to await the development of statistical thermodynamics and the subsequent development of quantum mechanics. Gibbs described the entropy of a system as being its "mixed-up-ness". The increase in the entropy of the substance which accompanies melting correlates with the corresponding increase in the degree of disorder of the configurational states of its constituent particles. In this brief introduction to statistical thermodynamics, this chapter considers the microcanonical cases. Statistical thermodynamics postulates that the equilibrium state of a system is simply the most probable of all of its possible microstates. The chapter discusses a general derivation of the Boltzmann distribution for a large number of particles among various energy levels. The Boltzmann equation thus provides a qualitative understanding of entropy. Classical thermodynamics shows that the transfer of thermal energy from a body at some temperature to a body at a lower temperature is an irreversible process which is accompanied by the production of entropy.