Invariant Entropy and Complexity of Quantum States

The concept of entropy is fundamental for many branches of physics and other sciences dealing with systems which reveal a certain degree of complexity and disorder. As stressed in the monograph 1, ‘‘entropy is not a single concept but rather a family of notions". In relation to quantum theory, the mainstream of development is formed by four main overlapping lines. They can be referred to as thermodynamical (Boltzmann Gibbs) entropy, quantum ensemble (von Neumann) entropy, information (Shannon) entropy and dynamical (Kolmogorov Sinai) entropy. Since the general description of a quantum system, including its interaction with the environment, time development and relaxation to equilibrium, can be given in terms of the density matrix , the von Neumann definition,