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Entropy production and nonequilibrium stationarity in quantum dynamical systems

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TLDR
In statistical physics, the linear response theory is well known as the most effective method, in the linear-approximation regimes, of calculating transport coefficients which describe dissipative aspects in the macroscopic manifestations of microscopic quantum systems.
Abstract
In statistical physics, Kubo's linear response theory is well known as the most effective method, in the linear-approximation regimes, of calculating transport coefficients which describe dissipative aspects in the macroscopic manifestations of microscopic quantum systems. From the viewpoint of the mutual relationship between the microscopic and macroscopic levels, it is clear that the response theory is essentially concerned with the information-theoretical problems. For lack of such key-concepts as entropy and/or entropy production, however, this theory has long been taken in physics merely as a calculational device, without the deep understanding of the reason for its general validity.

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Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

TL;DR: In this paper, the authors review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics and introduce notions of entropy production and heat fluxes, and study their properties in a model of a small finite quantum system coupled to several independent thermal reservoirs.
Journal ArticleDOI

Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs

TL;DR: In this article, the authors studied the non-equilibrium statistical mechanics of a 2-level quantum system coupled to two independent free Fermi reservoirs, which are in thermal equilibrium at inverse temperatures β1≠β2.
Journal ArticleDOI

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

TL;DR: In this article, a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields) is studied, and it is shown that the combined system has a family of stationary states parametrized by two numbers, T1 and T2 (reservoir temperatures).
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A note on the Landauer principle in quantum statistical mechanics

TL;DR: In this article, it was shown that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than kT log 2.
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A note on the Landauer principle in quantum statistical mechanics

TL;DR: In this paper, it was shown that Landauer's bound saturates under a natural ergodicity assumption on the joint system S+R for adiabatically switched interactions.
References
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Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems

TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Journal ArticleDOI

Markovian master equations

TL;DR: In this article, the memory effects in a quantum-mechanical master equation become negligible in the weak coupling limit for a finite-dimensional system weakly coupled to an infinite free heat bath.
Journal ArticleDOI

On the equilibrium states in quantum statistical mechanics

TL;DR: In this article, the authors studied the representation of the C*-algebra of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ and showed that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant.
Journal ArticleDOI

Quantum-mechanical perturbations giving rise to a statistical transport equation

TL;DR: In this article, the authors considered the case of transport processes produced by a small perturbation and derived a greatly improved derivation of the transport equation, which avoids the repeated use of a random phase assumption after each of a long succession of short time intervals.
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