Based on the property of extensivity , we derive in a mathematically consistent manner the explicit expressions of the chemical potential μμ and the Clausius entropy S for the case of monoatomic ideal gases in open systems within phenomenological thermodynamics. Neither information theoretic nor quantum mechanical statistical concepts are invoked in this derivation. Considering a specific expression of the constant term of S, the derived entropy coincides with the Sackur–Tetrode entropy in the thermodynamic limit. We demonstrate, however, that the former (...) limit is not contained in the classical thermodynamic relations, implying that the usual resolutions of Gibbs paradox do not succeed in bridging the gap between the thermodynamics and statistical mechanics. We finally consider the volume of the phase space as an entropic measure, albeit, without invoking the thermodynamic limit to investigate its relation to the thermodynamic equation of state and observables. (shrink)

Based on the property of extensivity, we derive in a mathematically consistent manner the explicit expressions of the chemical potential and the Clausius entropy $S$ for the case of monoatomic ideal gases in open systems within phenomenological thermodynamics. Neither information theoretic nor quantum mechanical statistical concepts are invoked in this derivation. Considering a specific expression of the constant term of $S$, the derived entropy coincides with the Sackur-Tetrode entropy in the thermodynamic limit. We demonstrate however, that the former limit is (...) not contained in the classical thermodynamic relations, implying that the usual resolutions of Gibbs paradox do not succeed in bridging the gap between the thermodynamics and statistical mechanics. We finally consider the volume of the phase space as an entropic measure, albeit, without invoking the thermodynamic limit to investigate its relation to the thermodynamic equation of state and observables. (shrink)

The idea that, in the microscopic world, particles are indistinguishable, interchangeable and without identity has been central in quantum physics. The same idea has been enrolled in statistical thermodynamics even in a classical framework of analysis to make theoretical results agree with experience. In thermodynamics of gases, this hypothesis is associated with several problems, logical and technical. For this case, an alternative theoretical framework is provided, replacing the indistinguishability hypothesis with standard probability and statistics. In this framework, entropy is a (...) probabilistic notion applied to thermodynamic systems and is not extensive per se. Rather, the extensive entropy used in thermodynamics is the difference of two probabilistic entropies. According to this simple view, no paradoxical behaviors, such as the Gibbs paradox, appear. Such a simple probabilistic view within a classical physical framework, in which entropy is none other than uncertainty applicable irrespective of particle size, enables generalization of mathematical descriptions of processes across any type and scale of systems ruled by uncertainty. (shrink)

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a ‘quantum connection’ stubbornly persists in the literature, (...) even though it has also been criticized frequently. Here we shall argue that although this criticism is justified, the proposed alternative solutions have often been wrong and have not put the paradox in its right perspective. In fact, the Gibbs paradox is unrelated to fundamental issues of particle identity; only distinguishability in a pragmatic sense plays a role , and in principle the paradox always is there as long as the concept of a particle applies at all. In line with this we show that the paradox survives even in quantum mechanics, in spite of the quantum mechanical symmetrization postulates. (shrink)

Even though the second law of thermodynamics holds the supreme position among the laws of nature, as stated by many distinguished scientists, notably Eddington and Einstein, its position appears to be also quite peculiar. Given the atomic nature of matter, whose behavior is well described by statistical physics, the second law could not hold unconditionally, but only statistically. It is not an absolute law. As a result of this, in the present paper we try to argue that we have not (...) yet any truly cogent argument to exclude its possible macroscopic violation. Even Landauer's information-theoretic principle seems to fall short of the initial expectations of being the fundamental ‘physical’ reason of all Maxwell's demons failure. Here we propose a modified Szilard engine which operates without any steps in the process resembling the creation or destruction of information. We argue that the information-based exorcisms must be wrong, or at the very least superfluous, and that the real physical reason why such engines cannot work lies in the ubiquity of thermal fluctuations.We see in the above peculiar features the main motivation and rationale for pursuing exploratory research to challenge the second law, which is still ongoing and probably richer than ever. A quite thorough description of some of these challenges is also given. (shrink)

Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical mechanics should be revised, either on the basis of quantum mechanics or on the basis of general and fundamental considerations about the distinguishability of particles. In this article we argue against this response. We show that both the extensive thermodynamic and the non-extensive statistical entropy are (...) perfectly alright within their own fields of application. Changes in the statistical formulas that remove the discrepancy must be seen as motivated by pragmatic reasons rather than as justified by basic arguments about particle statistics. (shrink)