Abstract
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of reduction and emergence.
Highlights
Thermodynamics and statistical mechanics coexist in a collaborative relationship within the envelope of thermal physics
We have presented a picture of the way that thermodynamics and statistical mechanics coexist and collaborate within the envelope of thermal physics
We showed that the relationship between the two developments, represented by the columns in Fig. 1 depends, on the one hand, on inter-theory connecting relationships from thermodynamics to statistical mechanics, one of which, FTD–3, can, in the context of deductive reduction be regarded as a bridge law, with the remaining two, FTD–1 and FTD–2, being consequences of FTD–3
Summary
Thermodynamics and statistical mechanics coexist in a collaborative relationship within the envelope of thermal physics. In many presentations of the subject, in undergraduate texts, it is heuristically advantageous to intermingle the macroscopic concepts of thermodynamics with the micro-picture provided by statistical mechanics. It is, self-evident that statistical mechanics needs the basic structure of thermodynamics with inter-theory connecting relationships defining the thermodynamic quantities like internal energy, temperature and entropy. There are some advantages, both aesthetic and mathematical, in producing an account of thermodynamics which makes no reference to the underlying microstructure of the system, as would seem to be one of the aims of
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