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Foundations of Physics

A unified quantum theory of mechanics and thermodynamics. Part IIa. Available energy

George Hatsopoulos, Elias P. Gyftopoulos

Published Apr 1, 1976• 75 citations
Publisher
DOI
10.1007/bf00708955

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Abstract Part II of this two-part paper refutes the beliefs about the statistical interpretation of thermodynamics, and the association of entropy with disorder that are summarized in Part I. The refutation of the statistical approach is based on either a nonstatistical unified quantum theory of mechanics and thermodynamics, or an almost equivalent, novel, nonquantal exposition of thermodynamics. Entropy is shown to be: (i) valid for any system (both macroscopic and microscopic, including one-particle systems), and any state (both thermodynamic or stable equilibrium, and not stable equilibrium); (ii) a measure of the quantum-theoretic pliable shape of the molecules of a system; and (iii) a monotonic indicator of order. In contrast to statistics which associates a thermodynamic equilibrium macrostate with the largest number of compatible microstates, the second law avers that, for each set of values of energy, volume, and amounts of constituents of either a macroscopic or a microscopic system, there exists one and only one thermodynamic or stable equilibrium state. So, even if Boltzmann’s definition were used, a thermodynamic equilibrium state is one of perfect order.

ASME International Mechanical Engineering Congress and Exposition (IMECE)•Nov 14, 1999•0 citations
The purpose of this paper is to discuss the hypothesis that the second law of thermodynamics and its corollaries are manifestations of microscopic quantum effects of the same nature but more general than those described by the Heisenberg uncertainty principle. This hypothesis is new to physics. Energy is a property of matter that has unified our understanding of physical phenomena. It appears prominently in both mechanical and thermodynamic theories. It is defined by the first law of thermodynamics, and its conservation is one of the keystones of analyses of both microscopic and macroscopic phenomena. Adiabatic availability--the amount of work that can be extracted from a system adiabatically--is also a property of matter but has not been accepted with the same unanimity as energy. Experience, especially with large bodies, indicates that not all the energy of a system is available in the form of work. For a given system, say atoms
Abstract Quantifying the ergotropy (also known as available energy), namely the maximal amount of energy that can be extracted from a thermally isolated system, is a central problem in quantum thermodynamics. Notably, the same problem has been long studied for classical systems as well, e.g. , in plasma physics and astrophysics, where the basic principles for its solution are known for the case of collisionless fluids. Here we provide the general analytical expression of ergotropy of classical systems valid regardless of their size and the type of interparticle interactions, and show that it emerges as the classical limit of the quantum expression of ergotropy, for quantum systems that are classically ergodic. We thus establish a unified theory of classical and quantum ergotropy, whose applicability ranges from atomic to galactic scale. Such unified theory is indispensable for studying the genuine quantum signatures of ergotropy: We show that the celebrated decomposition of quantum ergotropy into coherent ant inchoherent parts survives in the classical regime, indicating that coherences do not necessarily reveal quantumness. The unified theory also allows to port tools and methods across the classical-quantum boundary to unlock the solution of standing problems. We apply this to swiftly solve the open problem of ergotropy extraction in the classical regime.
Abstract Part II of this two-part paper refutes the beliefs about the statistical interpretation of thermodynamics, and the association of entropy with disorder that are summarized in Part I. The refutation of the statistical approach is based on either a nonstatistical unified quantum theory of mechanics and thermodynamics, or an almost equivalent, novel, nonquantal exposition of thermodynamics. Entropy is shown to be: (i) valid for any system (both macroscopic and microscopic, including one-particle systems), and any state (both thermodynamic or stable equilibrium, and not stable equilibrium); (ii) a measure of the quantum-theoretic pliable shape of the molecules of a system; and (iii) a monotonic indicator of order. In contrast to statistics which associates a thermodynamic equilibrium macrostate with the largest number of compatible microstates, the second law avers that, for each set of values of energy, volume, and amounts of constituents of either a macroscopic or a microscopic system, there exists one and only one thermodynamic or stable equilibrium state. So, even if Boltzmann’s definition were used, a thermodynamic equilibrium state is one of perfect order.