The notion that fundamental properties common to all energetic phenomena engender both thermodynamic entropy and quantum non-locality has been explored by the author in two previous papers, and a significant amount of research. This paper summarizes those results, including both ideas from those papers and more recent developments. The idea that entropy pertains to the dispersal – or spreading and sharing – of energy has been widely adopted in Chemistry texts, over the prior notion that entropy reflects disorder. However; the situation is very different in Physics where that question has been sidestepped by the adoption of a model based on information loss. The author believes it is time to re-visit this matter, as the tendency for energy to spread and be shared may be a fundamental property.
The notion that fundamental properties common to all energetic phenomena engender both thermodynamic entropy and quantum non-locality has been explored by the author in two previous papers, and a significant amount of research. This paper summarizes those results, including both ideas from those papers and more recent developments. The idea that entropy pertains to the dispersal – or spreading and sharing – of energy has been widely adopted in Chemistry texts, over the prior notion that entropy reflects disorder. However; the situation is very different in Physics where that question has been sidestepped by the adoption of a model based on information loss. The author believes it is time to re-visit this matter, as the tendency for energy to spread and be shared may be a fundamental property.
Abstract. Both researchers and educators have expressed displeasure with the definition of entropy as a measure of disorder. Instead, it is argued by Leff, Lambert, and others that the increase of entropy can be far more accurately described using terms such as ‘dispersal of energy, ’ ‘spreading and sharing of energy, ’ and ‘spatial and temporal spreading. ’ In decoherence theory, a similar metaphor is used to describe the phenomena involved with quantum non-locality, superposition, and entanglement. Specifically the wavefunction of a quantum entity, such as a sub-atomic particle or photon is not seen to collapse but rather is transferred through interactions to a system and/or its environment. This suggests there may be a common basis for entropy and non-locality. I explore the idea that energy is motive and extensive by nature, and that all its forms of expression involve motion, action, and propagation, which clearly leads to its being spread and shared when unconstrained, among the available microstates of its local system and the larger environment. Thus a single description, focusing on this universal quality of energy, explains both 2 nd Law entropy and quantum non-locality.
Abstract: Quantum-Mechanical objects and phenomena have a different nature, and follow a different set of rules, from their classical counterparts. Two interesting aspects are the superposition of states and the non-locality of objects and phenomena. A third aspect, that gives quantum-mechanical objects which have common roots a non-local connection, is quantum entanglement. This paper takes up the question of whether these three properties of quantum mechanical systems facilitate the action of entropy’s increase, in terms of creating a condition where energy is dispersing, or going from being localized to being more spread out over time. Quantum Mechanics gives each quantum entity the nature of a container or vehicle for both energy and information, some part of which is necessarily non-local. The author feels that quantum-mechanical systems take on aspects of computing engines, in this context. He discusses how the onset of chaos is possible with even the simplest calculational processes, how these processes also result in complexity building, and why both of these dynamics contribute to the character of entropy as observed in ordinary affairs, or with macroscopic systems.
Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicated details of the microscopic dynamics within a macroscopic system. The strength of thermodynamics lies in the universality provided by this paradigm. In contrast, quantum mechanics focuses on describing the dynamics of microscopic systems, aiming to make predictions about experiments we perform, a goal shared by all fundamental physical theories, which are often framed as gauge theories in modern physics. Recently, a gauge theory for quantum thermodynamics was introduced, defining gauge-invariant work and heat, and exploring their connections to quantum phenomena. In this work, we extend that theory in two significant ways. First, we incorporate energy spectrum degeneracies, which were previously overlooked. Additionally, we define gauge-invariant entropy, exploring its properties and connections to other physical and informational quantities. This results in a complete framework for quantum thermodynamics grounded in the principle of gauge invariance. To demonstrate some implications of this theory, we apply it to well-known critical systems.
In the scientific and engineering literature, entropy—the distinguishing feature of thermodynamics from other branches of physics—is viewed with skepticism, and thought to be not a physical property of matter—like mass or energy—but a measure either of disorder in a system, or of lack of information about the physics of a system in a thermodynamic equilibrium state, and a plethora of expressions are proposed for its analytical representation. In this article, I present briefly two revolutionary nonstatistical expositions of thermodynamics (revolutionary in the sense of Thomas Kuhn, The Structure of Scientific Revolutions, U. Chicago Press, 1970) that apply to all systems (both macroscopic and microscopic, including one spin or a single particle), to all states (thermodynamic equilibrium, and not thermodynamic equilibrium), and that disclose entropy as an intrinsic property of matter.The first theory is presented without reference to quantum mechanics even though quantum theoretic ideas are lurking behind the exposition. The second theory is a unified quantum theory of mechanics and thermodynamics without statistical probabilities, that is, I am not presenting another version of statistical quantum mechanics.
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories including matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it. We focus on both of purely information-theoretic concepts and their physical implications: We present self-contained and rigorous proofs of several fundamental properties of entropies, divergences, and majorization. We also discuss the modern formulations of thermodynamics, especially from the perspectives of stochastic thermodynamics and resource theory of thermodynamics. Resource theory is a recently-developed field as a branch of quantum information theory in order to quantify (energetically or information-theoretically) "useful resources." We show that resource theory has an intrinsic connection to various fundamental ideas of mathematics and information theory. This book is not intended to be a comprehensive review of the field, but would serve as a concise introduction to several important ingredients of the information-theoretic formulation of thermodynamics.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.