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Open Access item New Microscopic Connections of Thermodynamics 
Authors:  Plastino, A. Casas, Montserrat 
Issue Date:  Jan2011 
Publisher:  InTech 
Citation:  Thermodynamics 120 (2011) 
Abstract:  This is a work that discusses the foundations of statistical mechanics (SM) by revisiting its
postulates in the case of the two main extant versions of the theory. A third one will here
we added, motivated by the desire for an axiomatics that possesses some thermodynamic
“flavor”, which does not happen with neither of the two main SM current formulations,
namely, those of Gibbs’ (1; 2), based on the ensemble notion, and of Jaynes’, centered on
MaxEnt (3; 4; 5).
One has to mention at the outset that we “rationally understand” some physical problem
when we are able to place it within the scope and context of a specific “Theory”. In turn, we
have a theory when we can both derive all the known interesting results and successfully
predict new ones starting from a small set of axioms. Paradigmatic examples are von
Neumann’s axioms for Quantum Mechanics, Maxwell’s equations for electromagnetism,
Euclid’s axioms for classical geometry, etc. (1; 3).
Boltzmann’s main goal in inventing statistical mechanics during the second half of the XIX
century was to explain thermodynamics. However, he did not reach the axiomatic stage
described above. The first successful SM theory was that of Gibbs (1902) (2), formulated on the
basis of four ensemblerelated postulates (1). The other great SM theory is that of Jaynes’ (4),
based upon the MaxEnt axiom (derived from Information Theory): ignorance is to be extremized
(with suitable constraints).
Thermodynamics (TMD) itself has also been axiomatized, of course, using four macroscopic
postulates (6). Now, the axioms of SM and of thermodynamics belong to different worlds
altogether. The former speak of either “ensembles” (Gibbs), which are mental constructs,
or of “observers’ ignorance” (Jaynes), concepts germane to thermodynamics’ language, that
refers to laboratoryparlance. In point of fact, TMD enjoys a very particular status in the whole
of science, as the one and only theory whose axioms are empirical statements (1).
Of course, there is nothing to object to the two standard SMaxiomatics referred to
above. However, a natural question emerges: would it be possible to have a statistical
mechanics derived from axioms that speak, as far as possible, the same language as that of
thermodynamics? To what an extent is this feasible? It is our intention here that of attempting
a serious discussion of such an issue and try to provide answers to the query, following ideas
developed in (7; 8; 9; 10; 11; 12; 13). 
Publisher version (URL):  http://www.intechopen.com/articles/show/title/newmicroscopicconnectionsofthermodynamics 
URI:  http://hdl.handle.net/10261/46146 
ISBN:  9789533075440 
Appears in Collections:  (IFISC) Libros y partes de libros

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