Mixing indistinguishable systems leads to a quantum Gibbs paradox

The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an “ignorant” observer, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.

THE LOGICAL CONTRADICTIONS OF THE TIME REVERSIBILITY AND THEIR SOLUTIONS IN PHILOSOPHY AND SCIENCE OF XX-XXI CENTURIES

Introduction:the purpose of this article is to highlight the main difficulties and paradoxes, which connected with the time reversibility and also to research their solutions in the context of philosophy and natural science. The article focus is the main philosophical and scientific ideas of this problem of XX-XXI centuries.Materials and Methods:the base of this article is various developments of Russian and foreign researchers, who researched problem of the time reversibility with different approaches. The main chosen methods are critical analysis of the researched materials and the attempt on this base to synthesize identified contradictions and their solutions.Results:the interim result of this article is the statement that time reversibility is not logically controversial, but it is improbable. It was also noticed that the definition of time reversibility and the definition of time are a problem, therefore the possibility to speak about existing in nature or non-existing of the phenomenon depends on the researcher’s point of view.If we assume the possibility of time reversibility there appear a few paradoxes, which are Gibbs’ paradox, time’s multiplicity, causality leap, dead grandfather paradox.Not only philosophers and scientists were interested in those paradoxes, but also science-fiction writers who offered their own solutions. Today the Edinburg University philosophers and particularly A. Richmond are dealing with the problem, they also created the new direction of the philosophy named time travel philosophy. Richmond’s, his predecessors’ and Russian and foreign colleagues’ developments are presented in the paper; the attempt to find the contradictions in their approaches and the ways of its resolving has been also made.Discussion and conclusions: the main contradictions concerning the time reversibility are not ultimately resolved and still exist as a field for further discussion.

The Gibbs Paradox

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs’ notion of ‘generic phase’). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction.

The Gibbs Paradox: Early History and Solutions

This article is a detailed history of the Gibbs paradox, with philosophical morals. It purports to explain the origins of the paradox, to describe and criticize solutions of the paradox from the early times to the present, to use the history of statistical mechanics as a reservoir of ideas for clarifying foundations and removing prejudices, and to relate the paradox to broad misunderstandings of the nature of physical theory.