Abstract
Traditional answers to what the 2nd Law is are well known. Some are based on the microstate of a system wandering rapidly through all accessible phase space, while others are based on the idea of a system occupying an initial multitude of states due to the inevitable imperfections of measurements that then effectively, in a coarse grained manner, grow in time (mixing). What has emerged are two somewhat less traditional approaches from which it is said that the 2nd Law emerges, namely, that of the theory of quantum open systems and that of the theory of typicality. These are the two principal approaches, which form the basis of what today has come to be called quantum thermodynamics. However, their dynamics remains strictly linear and unitary, and, as a number of recent publications have emphasized, “testing the unitary propagation of pure states alone cannot rule out a nonlinear propagation of mixtures”. Thus, a non-traditional approach to capturing such a propagation would be one which complements the postulates of QM by the 2nd Law of thermodynamics, resulting in a possibly meaningful, nonlinear dynamics. An unorthodox approach, which does just that, is intrinsic quantum thermodynamics and its mathematical framework, steepest-entropy-ascent quantum thermodynamics. The latter has evolved into an effective tool for modeling the dynamics of reactive and non-reactive systems at atomistic scales. It is the usefulness of this framework in the context of quantum thermodynamics as well as the theory of typicality which are discussed here in some detail. A brief discussion of some other trends such as those related to work, work extraction, and fluctuation theorems is also presented.
Highlights
New experimental evidence (e.g., [1,2,3,4,5,6,7,8,9,10]) over the last three decades has seen the emergence at atomistic scales of the phenomenon of “spontaneous decoherence”, which in turn has led to a revival of interest in matters related to the unitary foundations of quantum mechanics (QM) and what if anything the 2nd Law of thermodynamics may have to say about this
All researchers are utterly used to the 2nd Law, even if not agreed on what it is and from where it comes, the idea of almost any system always approaching a state of stable equilibrium, which for example, from a quantum statistical mechanical (QSM)
This paper has examined in some detail the theory of typicality, which is one of the two principal orthodox approaches that form the basis of what today is called quantum thermodynamics
Summary
New experimental evidence (e.g., [1,2,3,4,5,6,7,8,9,10]) over the last three decades has seen the emergence at atomistic scales of the phenomenon of “spontaneous decoherence”, which in turn has led to a revival of interest in matters related to the unitary foundations of quantum mechanics (QM) and what if anything the 2nd Law of thermodynamics may have to say about this. As argued in [56], what could be said of all or some of these preparations is that they must be considered physically equivalent if no conceivable local measurement can be devised to distinguish between them Another useful mathematical framework within the quantum thermodynamic formalism is that which formulates the probability density distribution of an atomistic level system in terms of position and momentum and its momentum spectrum as discrete [57]. Such a formulation becomes useful when the thermal de Broglie wave length of particles is no longer negligible in comparison with system size In this case, quantum size effects (QSE) appear and considerably change the thermodynamic behavior of systems, especially near internal and external walls so that size and shape become additional parameters in the thermodynamic state function resulting in a number of effects not seen in large systems, e.g., quantum surface energy, anisotropic gas pressure, diffusion driven by size difference, quantum boundary layers, quantum forces, thermosize effects, etc. Before describing this framework and its applications, we begin with a detailed discussion of the typicality approach to quantum thermodynamics
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