Entropy and Principle of Maximum Entropy

Clausius coined the term ‘entropy’ from the Greek meaning transformation. Thus, entropy originated in physics and occupies an exceptional position among physical quantities. It does not appear in the fundamental equations of motion. Its nature is, rather, a statistical or probabilistic one, for it can be interpreted as a measure of the amount of chaos within a quantum mechanical mixed state. It is an extensive property like mass, energy, volume, momentum, charge, number of atoms of chemical species, etc., but, unlike these quantities, it does not obey a conservation law. Entropy is not an observable; rather it is a function of state. For example, if the state is described by the density matrix, its entropy is given by the van Neumann formula. In physical sciences, entropy relates macroscopic and microscopic aspects of nature and determines the behavior of macroscopic systems in equilibrium.