In this chapter we start with methodological analysis of the notion of scientifictheory and its interrelation with reality. This analysis is based onthe works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviewsof D’ Agostino). Following Helmholtz, Hertz established the “Bild concept”for scientific theories. Here “Bild” (“picture”) carries the meaning “model”(mathematical). The main aim of natural sciences is construction of thecausal theoretical models (CTMs) of natural phenomena. Hertz claimed thatCTM cannot be designed solely on the basis of observational data; it typicallycontains hidden quantities. Experimental data can be described by anobservational model (OM), often at the price of acausality. CTM-OM interrelationcan be tricky. Schrödinger used the Bild concept to create CTM forquantum mechanics (QM) and QM was treated as OM. We follow him andsuggest a special CTM for QM, the so-called prequantum classical statisticalfield theory (PCSFT). QM can be considered as a PCSFT-image, but notas straightforward as in Bell’s model with hidden variables. The commoninterpretation of the violation of the Bell inequality is criticized from theperspective of the two-level structuring of scientific theories.

The physical origins of entropy are explained. Configurational entropy in the point approximation was used previously, but Chapter 7 shows how configurational entropy can be calculated more accurately with cluster expansion methods, and the pair approximation is developed in some detail. Atom vibrations are usually the largest source of entropy in materials, and the origin of vibrational entropy is explained in Section 7.4. Vibrational entropy is used in new calculations of the critical temperatures of ordering and unmixing, which were done in Chapter 2 with configurational entropy alone. For metals there is a heat capacity and entropy from thermal excitations of electrons near the Fermi surface, and this increases with temperature. At high temperatures, electron excitations can alter the vibrational modes, and there is some discussion about how the different types of entropy interact.

Planck immediately set about attempting to understand the significance of his formula for black-body radiation. He began by using Boltzmann's procedure in statistical mechanics, an approach he had previously rejected, but then adopted empirically a definition of the entropy of the oscillators which introduced the concept of quantisation. HIs derivation was not understood by his contemporaries, including Einstein, because of the lack of a theoretical motivation for the definition of entropy. Despite a major effort to understand his formula, Planck found no classical solution to the meaning of h, Planck's constant.