Gibbs’ paradox

The entropy of mixing ideal gases was treated already by Gibbs. The result is known as the Gibbs paradox. Several scientists were engaged with this paradox, among them Rayleigh, Lorentz, Einstein, and von Neumann [1,2]. 

The paradox states that the two gases can be as similar as possible, but not completely similar to exhibit an entropy of mixing. Gibbs paradox was tried to be explained in several ways. For example, it was stated that nature changes the properties in jumps, in other words, in quanta [3, p. 163]. 

it has been argued that substances cannot become arbitrarily similar because they consist of isotopes. In contrast, in the case of o- and p-hydrogen, the difference of these compounds relies not on isotopes, but on their spins. Further, in polymers, an unsaturated end group, with either cis or trans, can be relevant that two kinds of compounds can be identified. However, the difference can be made essentially arbitrarily small as the molecular weight of the polymer increases. 

Gibbs paradox silently assumes that the components to be mixed have the same temperature. 

Therefore, similarity is not a continuous process as Gibbs believed. A more recent attempt to explain Gibbs paradox stresses the reversible and irreversible mixing [2], The chapter also reviews previous views. 

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GIBBS PARADOX. When two samples of the same gas at a given temperature and pressure are allowed to mingle by the removal of a... 

Considerations of the real sense of the Gibbs Paradox are used to illustrate the idea of the term step-aside which is our main methodological tool for looking for the infinite cycle in a Turing computing process and which enables us to avoid the commonly used attempts to solve the Halting Problem. 

Gibbs Paradox and Auto-Reference in Observation and Information Transfer... 

Let, in compliance with the solution of Gibbs Paradox, the integration constant S0 be the (change of) entropy AS which is added to the entropy a to figure out the measured entropy Sclaus of the equilibrium state of the system A (the final state of Gay-Lussac experiment) at a temperature 0. We have shown that without such correction, the less entropy o is evidenced,... 

Our observation of the equilibrium system A, including the mathematical correction for Gibbs Paradox, is then describable by the Shannon transfer scheme [ X, K.,Y ] where... 

We conclude by that, the diminishing of the measured entropy value about AS against S awaited, evidenced by Gibbs Paradox, does not originate in a watched system itself. Understood this way, it is a contradiction of a gnozeologic character based on not respecting real properties of any observation [6]. And, this means the following. 

For this all we need a certain step-aside from the system A expressed by the value r<°°, but, nevertheless with respecting properties of this step-aside, we do not fall into Gibbs Paradox [even when our railngs of diafragmas in the mode given r e (1,°°) is laid down]. 

Hejna, B. Gibbs Paradox as Property of Observation, Proof of II. Principle of Thermodynamics. In AIP Conf. Proc., Computing Anticipatory Systems CASYS 09 Ninth International Conference on Computing, Anticipatory Systems, 3-8 August 2009 Dubois, D., Ed. American Institute of Physics Melville, New York, 2010 pp 131-140. ISBN 978-0-7354-0858-6. ISSN 0094-243X. 

Lin, S.-K. (1996) Molecular diversity assessment logarithmic relations of information and species diversity and logarithmic relations of entropy and indistinguishability after rejection of Gibbs paradox of entropy mixing. Molecules, 1, 57-67. 

Gibbs paradox arises from the unsound assumption that the entropy of each gas in an ideal mixture is independent of the presence of the other gases ... 

On the other hand, it has been pointed out that Gibbs paradox is not really a paradox [7, 8]. The paradox seems to arise because the conditions of the process of mixing are not fixed properly. Coarsely spoken we can disparage what is happening as follows two different gases are mixed and the correct entropy of mixing is obtained. 

To illustrate the problem of Gibbs paradox more clearly, we introduce now a thermodynamic cycle that involves a chemical reaction. di-2-Butene has a boiling point of 4 °C and frans-2-butene has a boiling point of 1 °C. 

The Gibbs paradox arises from the idea that in the two chambers are singlecomponent gases and that the different gases could approach asymptotically to an indistinguishable gas. It is opposed from the nature of matter, since it is built from electrons, protons, and neutrons, it is not possible to approach the properties continuously. There can be only one electron added or removed. Thus, the change of the nature of the gases cannot be performed in arbitrary small steps. 

Tataiin, V, Borodiouk, O. Entropy calculation of reversible mixing of ideal gases shows absence of Gibbs paradox. Entropy 1(2), 25-36 (1999). [electronic] www.mdpi.org/entropy/... 

Ben-Naim, A. On the so-called Gibbs paradox, and on the real paradox. Entropy 9, 132-136 (2007). [electronic] http //www.mdpi.org/entropy/papers/e9030132.pdf Jaynes, E.T The Gibbs paradox. In C.R. Smith, G.J. Erickson, P.O. Neudorfer (eds.) Maximum Entropy and Bayesian Methods, Fundamental Theories of Physics, vol. 50, pp. 1-22. Kluwer Academic Publishers, Dordrecht, Holland (1992)... 

The Gibbs paradox, in C. R. Smith et al., eds., Maximum Entropy and Bayesian Methods, Seattle Kluwer Academic Publishers, pp. 1-21. 

To explain the Gibbs paradox and to prove the 11. P.T. we use the concept of bound information (2 15). This method is identical with introducing the Boltzman function of statistical physics. Its negative value, determined by a detailness of our description of an observed system, is proved to be a value of Clausius entropy (in a certain substitute equivalent equilibrium thermod5mamic way (19)). We show that a physical realization of such observation is equivalent to a scheme of a relevant (reversible) heat cycle (7). Its properties are expressible in terms of the Gibbs paradox. 

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