Open Quantum Matter-field Systems and Entropy (original) (raw)
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Open Quantum Systems of Particles and Principle 2 of Thermodynamics
We consider quantum master equations for a system of Fermions and an electromagnetic field, and apply these equations to a superradiant semiconductor structure converting environmental heat into coherent electromagnetic energy. For a non-irradiative system, these equations describe a time evolution with entropy increase, according to principle 2 of thermodynamics. However, for a superradiant system, the entropy may decrease, while the asymptotic solution of these equations, corresponding to constant entropy, describes a field radiation on the account of environmental heat absorption by Peltier effect.
Dissipation and entropy production in open quantum systems
Journal of Physics: Conference Series, 2010
A microscopic description of an open system is generally expressed by the Hamiltonian of the form: Htot = Hsys + Henviron + Hsys−environ. We developed a microscopic theory of entropy and derived a general formula, so-called "entropy-Hamiltonian relation" (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by Hsys−environ for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space L := H ⊗ f H , where H denotes the ordinary Hilbert space while f H the tilde Hilbert space conjugates to H . We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of Hsys−environ on the representation space L , the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.
The role of interactions in open quantum systems and the second law of thermodynamics
Journal- Korean Physical Society
In open quantum systems, it is difficult to know whether the system is in equilibrium or nonequilibrium. In order to investigate the role of interactions between the system and its environment in open quantum systems, we derive a formula which relates the Hamiltonian of the system to entropy. In this formula, these interactions inside the system and the entropy of the system are not connected to each other; only these interactions between the system and its environment are related to the entropy. Thus, this formula enables us to discriminate the types of interactions between the system and its environment; one type of interaction increases the entropy of the system, and the other type of interaction does not change the entropy of the system. We find that a certain type of interaction between the system and its environment causes a nonequilibrium state of the system. The criteria for the types of interactions between the system and its environment are specifically given by studying the entropy.
Dynamics and Thermodynamics of Linear Quantum Open Systems
Physical Review Letters, 2013
We study the behavior of networks of quantum oscillators coupled with arbitrary external environments. We analyze the evolution of the quantum state showing that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime. We demonstrate two main results on thermodynamics: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (therefore, such refrigerators require non-linearity as a crucial ingredient, as proposed by Kosloff and others ). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities. PACS numbers: 03.65.Yz
Perspective on quantum thermodynamics
2016
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems,made up ofmicroscopic particles, in terms of a small number ofmacroscopic quantities, such aswork and entropy. As systems get ever smaller, fluctuations of these quantities become increasingly relevant, prompting the development of stochastic thermodynamics. Recently we have seen a surge of interest in exploring the quantum regime, where the origin offluctuations is quantum rather than thermal.Many questions, such as the role of entanglement and the emergence of thermalisation, lie wide open. Answering these questionsmay lead to the development of quantumheat engines and refrigerators, as well as to vitally needed simple descriptions of quantummany-body systems.
Quantum heat distribution in thermal relaxation processes
Physical Review E, 2019
We analyze the heat exchange distribution of quantum open systems undergoing a thermal relaxation that maximizes the entropy production. We show that the process implies a type of generalized law of cooling in terms of a time dependent effective temperature Tt. Using a two-point measurement scheme, we find an expression for the heat moment generating function that depends solely on the system's partition function and on the law of cooling. Applications include the relaxation of free bosonic and fermionic modes, for which closed form expressions for the time-dependent heat distribution function are derived. Multiple free modes with arbitrary dispersion relations are also briefly discussed. In the semiclassical limit our formula agrees well with previous results of the literature for the heat distribution of an optically trapped nanoscopic particle far from equilibrium.
Quantum thermodynamics of single particle systems
Scientific Reports, 2020
thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. in this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. the corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved. In the past decade, many efforts have been devoted to understand how, starting from an isolated quantum system evolving under Hamiltonian dynamics, equilibration and effective thermodynamics emerge at long times 1-5. On the other hand, the investigations of open quantum systems initiate interests on the issue of quantum thermodynamics taking place under the quantum evolution of open systems 6-20. The questions of how thermodynamics emerges from quantum dynamics, how do quantum systems dynamically equilibrate and thermalize, and whether thermalization is always reachable in quantum regime, are central and fundamental to research for quantum thermodynamics. However, a general theory of quantum thermodynamics that has conceptually no ambiguity in answering the above questions has not yet been obtained, because investigations in addressing above questions inevitably take various assumptions and approximations. In this paper, we will attempt to answer these questions by rigorously solving the quantum dynamics based on the exact master equation we developed recently for a large class of open quantum systems 21-25. Recall that thermodynamics is built with the hypothesis of equilibrium 26. Macroscopic systems at equilibrium are fully described by the relation between the internal energy E and a set of other extensive parameters, the entropy S, the volume V, and the particle number N i of different components i = 1, 2, ••• , magnetic moment M, etc.,
Coherent Transport and Dynamical Entropy for Fermionic Systems
2003
This paper consists in two parts. First we set up a general scheme of local traps in an homogeneous deterministic quantum system. The current of particles caught by the trap is linked to the dynamical behaviour of the trap states. In this way, transport properties in an homogeneous system are related to spectral properties of a coherent dynamics. Next we apply the scheme to a system of Fermions in the one-particle approximation. We obtain in particular lower bounds for the dynamical entropy in terms of the current induced by the trap.
Aapp Physical Mathematical and Natural Sciences, 2008
What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrödinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility, including Onsager reciprocity relations and maximal-entropy-generation nonequilibrium dynamics, which we believe provides the microscopic foundations of heat, mass and momentum transfer theories, including all their implications such as Bejan's Constructal Theory of natural phenomena.