Thermodynamic

Hidden Variables and Thermodynamics

 Alberto Mesquita Filho

Integração VII(24):68-70,2001
© 1995 - 2001

This section in Portuguese
Este artigo em português

 

Abstract. A representational approach to entropy is presented, relating the increase in the entropy of the universe to the production of entropins (= neutrins?), and the stability of systems in thermodynamics equilibrium to the elastic character of molecular collisions.

Resumo. Uma teoria representacional para a entropia é apresentada, relacionando o aumento da entropia do universo à produção de entropinos (= neutrinos?), e a estabilidade dos sistemas em equilíbrio termodinâmico ao caráter elástico das colisões moleculares em tais condições.

 

 

1. INTRODUCTION

////////Among the several ways of enunciating the first principle of thermodynamics, we can mention this one:

If a system is subdued to a cyclical transformation, work W produced near-by is equal to heat Q extracted from near-by, that is,

(1)

Equality (1) takes to the characterization of state property X whose dX differential is defined by:

(2)

////////Thermodynamics treatises usually identify X with E (E from energy) and call this E property internal energy. More careful people state that nothing can assure us that E is the same energy property defined in mechanics. In fact, according to Mario Bunge (1974), thermodynamics is the paragon of the theory of phenomenology, worried to describe not heat phenomena but very general properties and laws, with the help of high level constructs such as energy E and entropy S. As a consequence, and in order to be coherent with itself, it must not venture into representational fields. It is this characteristic that makes it a low risk theory; it was also one of the factors to convince Einstein to claim that classical thermodynamics is the only physical theory with universal contents, and ¾in the context of the applicability structure of its basic concepts¾ it will never be contested. This of course does not mean it will never be explained.

////////When we identity X with E, supposing E is the same energy studied in mechanics, we evolute from phenomenology to representation, an evolution which, according to Bunge (op. cit.), stands for the ultimate goal of theorization. In fact, this evolution is not without risk, and it is worthwhile to mediate on the Mario Schenberg’s opinion (1984) on two of the most discussed representational theories which tried to substitute for thermodynamics:

////////There is one point on which quantic mechanics has cast no light: the second principle of thermodynamics. This principle remains as mysterious as before. The law of  growth of entropy cannot be deduced either by classical mechanical statistics nor by quantic mechanical statistics. Here there is something which is basic but we cannot understand yet. When something gets too difficult it is high time to make it simple.

////////One of the most polemical themes in physics during the 30s was the possible existence of hidden variables - HV’s - of quantic physics. A survey of this subject was recently published by Brown (1983) in CiênciaHoje. The questioning proposed by Einstein ¾and fiercely contested by Bohr¾ has not been solved yet. Most physicians preferred Bohr’s instrumentalism, with the support of Von Newmann’s demonstration of a theorem which mathematically proved the non-existence of HV’s. As soon as Von Newmann’s work was published, there started to come out experimental confirmation of numberless HV’s, a number Einstein himself never dreamed of. Such HV’s included neutrons, neutrins and anti-matter.

////////From an epistemological point of view we might claim that the innocuity or inoperableness of Von Newmann’s theorem practically did not help Einstein’s position before Bohr. In fact, it only strengthened the idea of an open science, in opposition to the usefulness criteria defended by instrumentalists supporting Bohr.

////////Few people realized the actual reason for the duel between Einstein and Bohr. Actually, the former believed that the basis upon which quantic mechanics was built was condemned and required urgent reparation. And Bohr, as a great theoretician, knew that ¾with only very rare exceptions¾ the principles of a representational theory are not to be changed since even the slightest change might change its characterization as a whole. Both Einstein and Bohr surely knew that not one of the newly discovered HV’s increased or decreased their argumentation’s.

////////Recently (1993 and 1995) I defended the idea of a HV of a classical nature and not so innocuous in terms of electromagnetic information. In the rest of this paper I intend to present a brief survey of a second HV of this kind, which I shall call entropin.

 

2. NATURAL TRANSFORMATIONS

////////Let us accept that, in some natural transformation, the following relationship is valid:

D E = D X - D N

(3)

in which DE stands for the variation in the system’s actual internal energy, DX the apparent variation in the internal energy measured by

(4)

and DN a hypothetical quantity of energy lost by the system as entropins. Entropins would be hypothetical entities, perhaps particles, perhaps neutrins, and, the these latter, they would not normally be captured by molecules in the medium they cross. It is as if entropins were absorbed by a third system, alien to ordinary experimental methods.

////////After the definition of parameters, we still have to make DE, DX e DN compatible with the first law of thermodynamics (see above). And this does not seem to be difficult.

////////Firstly let us consider a system in an initial stage i in order we can take it to a final stage f  through either totally irreversible transformations. In one of them (A) the system simply receives heat and loses entropins; therefore,

DAE  =

and in the other one (B), instead of head, the system receives work in an irreversible way, that is:

DBE  =

As D_AE  = D_BE, we can write:

(5)

////////In terms of equivalent transformations, the first law of thermodynamics lead us to conclude that

Consequently,

That is, if N is real, the first law of thermodynamics can assure us that whatever the process, since it is totally irreversible, ò¶N is independent from the mode and, therefore, ¶N is an exact differential, and N is a stage function of the system. Which is coherent with expression (3).

////////In a reversible process, the identity ¶n º dN is not to occur. That is, in order the universe being studied may return to its primitive situation, ò¶N must be equal to zero. And under these conditions, if we combine equations (2), (3) and (4), we must have

DE = ò dE = ò (¶X_rev - ¶N_rev)

////////= ò ¶X_rev = ò (¶Q_rev - ¶W_rev) .

////////If we compare a reversible process and a totally irreversible one whose proving system has the same initial and final stages, we shall have

DE = ò (¶Q - ¶W - ¶N)irrev = ò (¶Q - ¶W)rev

(6)

If both transformations simply involve changes of heat such as the isochoric transformation of a gas, expression (6) is simplified to

ò (¶Q - ¶N)_irrev = ò ¶Q_rev

or

ò ¶N_irrev = ò (¶Q_irrev - ¶Q_rev)

////////Which is by no means an interesting conclusion since, at least theoretically, it allows the experimental calculation of DN. We are still to know if ¶Qirrev and ¶Qrev are considerably different or if they have a different which can be proved at a laboratory, which unquestionably would support the model we presented.

////////Another interesting comparison is the isotermic expansion of an ideal gas through reversible and irreversible ways. In this case we shall have

DE = ò (-¶N)_irrev = ò (¶Q_rev - ¶W_rev)

/As ¶Q_rev  =  TDS and ¶W_rev =  DA, in which T = absolute temperature, S = entropy and A = Helmholtz’s free energy, we can write

DN = DA - TDS (isothermal expansion)

When a gas is isothermally expanded, it loses its capacity to do work with a value equal to DA. If the process is irreversible, the outside receives work, and the variation in external entropy compensates for the increase in entropy of the system. If the process is irreversible, the exterior shall not apparently be modified; at least the measurable exterior. Then we say that the entropy of the system and, therefore, the entropy of the universe increase. Of course, entropin are outside the classical conception of entropy if not outside the classical experimental universe

3. DISCUSSION AND CONCLUSIONS

I believe that every irreversible process, that is, all natural changes ¾such as a gas expansion, the inelastic shock, chemical reaction, mixing processes, etc.¾ follow the liberation of entropins (neutrinos?). But something is still to be made clear: how can the same final state be achieved through such different ways? That is, what does an isolated thermodynamically system loses instead of entropins when the resulting transformation is reversible?

The reversible process is characterized by the discrete changes in heat and/or work. These changes are related to molecule collisions. Thus, I would say that intense collisions liberate entropins and, therefore, they are irreversible. And discrete collisions are not but friendly meetings in which a molecule transfers photons to another one; or, in or order use a classical language, the molecule with lesser kinetic energy catches the radiant energy from the molecule with lesser kinetic energy.

Reversible processes are those in which molecule collisions are 100% elastic. And this only occurs in balanced systems, that is, where the pattern shift of the average molecule kinetic energy does not go beyond a certain critical level.

BIBLIOGRAPHY

 BROWN, H., A. (1983), Estranha Natureza da Realidade Quântica, Ciência Hoje, vol. 2, n.° 7.

BUNGE, M. (1974), Teoria e Realidade, Ed. Perspectiva, São Paulo.

EINSTEIN, A., Notas Autobiográficas, Ed. Nova Fronteira, R.J.

MESQUITA F.°, A. (1984), Os Átomos Também Amam, Editora das Faculdades São Judas Tadeu, São Paulo.

-----(1987), Confesso Que Blefei ¾ Física Antiga × Moderna, Editora das Faculdades São Judas Tadeu, São Paulo.

-----(1993), A Equação do Elétron e o Eletromagnetismo, Editora Ateniense, São Paulo.

-----(1995), Sobre a Natureza Físico-Matemática do Elétron, Integração II(4):26-30,1995, São Paulo.

SCHENBERG, M. (1984), Pensando a Física, Ed. Brasiliense, São Paulo.