Quantum-Mechanical Framework

Rudra Pandey

In this paper we introduce a mathematical framework, developed within the extended classical mechanics setup , which helps us derive quantum nature and the relation E = hν from it. By doing so, we give a solid mathematical foundation to quantum nature and remove the inherent incompatibilities between classical mechanics and quantum mechanics. We also derive Schrödinger's equation with the help of this framework to establish the validity of this framework.

Tiago F. F. Santos, Camille Latune

Traditional quantum thermodynamic frameworks associate work to energy exchanges induced by unitary transformations generated by external controls, and heat to energy exchanges induced by bath interaction. Recently, a framework was introduced aiming at extending the thermodynamic formalism to genuine quantum settings, also referred to as autonomous quantum systems: free from external controls, only quantum systems interacting with each other. In this paper, we apply such a thermodynamic framework to common experimental situations of interacting quantum systems. In situations where traditional frameworks detect only heat exchanges, the recent autonomous thermodynamic framework points at work exchanges based on two mechanisms: population inversion and coherence generation / consumption. Such mechanisms are well known in the literature for being related to work expenditure and extraction, in particular in relation with ergotropy, which emphasizes the relevance of the autonomous framework and the limitations of traditional ones. Furthermore, the autonomous framework also identifies a genuine non-unitary mechanism of work exchange related to athermality. %, also pointed out as a resource for work extraction. Finally, in the semi-classical limit, the autonomous framework identifies all energy exchanges as pure work, but distinguishes between local work and interaction energy. Our results show that the autonomous framework provides a refined analysis of work exchange mechanisms in the quantum realm and serves as a consistent approach to analyze thermodynamic processes in realistic quantum devices.

Stephen L. Adler

Abstract We proceed now to give the basic kinematic and dynamical framework of quaternionic quantum mechanics. In much of what follows there is a close analogy with the familiar framework of complex quantum mechanics, but there are a number of characteristic features of the quaternionic case that play a significant role in the sequel, and to which we alert the reader.

Arif Ahmed