Some non-equilibrium invariant states for the asymmetric exclusion QMS at level one

2015 ◽  
Vol 18 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Julio C. García ◽  
Fernando Guerrero-Poblete
Keyword(s):  
Detailed Balance ◽  
Necessary Condition ◽  
Invariant State ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Starting Point ◽  
Invariant States ◽  
Asymmetric Exclusion ◽  
The One ◽  
Non Equilibrium

We review the Asymmetric Exclusion QMS in the light of new results, taking as a starting point the dynamics in the one particle space. We give a condition for the Asymmetric Exclusion QMS to be conservative, prove that an invariant state is necessarily diagonal and give conditions on eigenvalues of such an invariant state. We also give, a necessary condition to annul the generator of the predual semigroup; with this and the weighted detailed balance condition, we propose a method to construct some non-equilibrium invariant states.

Entropy, fluctuation and transport in lattice gas systems with generalized semi-detailed balance

1997 ◽  
Vol 57 (1) ◽  
pp. 175-185 ◽  
Author(s):  
HUDONG CHEN
Keyword(s):  
Lattice Gas ◽  
Detailed Balance ◽  
Statistical Properties ◽  
Continuous Systems ◽  
Physical Processes ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Dirac Type ◽  
Reciprocity Relations ◽  
Non Equilibrium

We describe the existence of an entropy for lattice gas systems of Fermi–Dirac type based on a generalized semi-detailed balance condition. We demonstrate some essential equilibrium and non-equilibrium fluctuation and dissipation properties, including the so-called Onsager's reciprocity relations, as a consequence of this condition. Requirements for the existence of certain statistical properties in discrete lattice gas systems are not directly inferred from those in real continuous systems, but are closely related. Hence understanding in detail the causes and results for lattice gas systems may provide further insights into fundamental microscopic physical processes.

Non-equilibrium thermodynamics of quantum bipartite system

2021 ◽  
pp. 2150294
Author(s):  
Kuan-Meng Zhang ◽  
Yi-Xin Chen
Keyword(s):  
Detailed Balance ◽  
Quantum Thermodynamics ◽  
Equilibrium Thermodynamics ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Bipartite System ◽  
Hamiltonian Model ◽  
Thermodynamics And Statistical Mechanics ◽  
Non Equilibrium

In quantum information and quantum computation, a bipartite system provides a basic few-body framework for investigating significant properties of thermodynamics and statistical mechanics. A Hamiltonian model for a bipartite system is introduced to analyze the important role of interaction between bipartite subsystems in quantum non-equilibrium thermodynamics. We illustrate discrimination between such quantum thermodynamics and classical few-body non-equilibrium thermodynamics. By proposing a detailed balance condition of the bipartite system, we generally investigate the properties of the entropy and heat of our model, as well as the relation between them.

Invariant States for a Quantum Markov Semigroup Constructed from Quantum Bernoulli Noises

2018 ◽  
Vol 25 (04) ◽  
pp. 1850019
Author(s):  
Jinshu Chen
Keyword(s):  
Commutation Relation ◽  
Detailed Balance ◽  
Markov Semigroup ◽  
Equal Time ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
The Family ◽  
Invariant States ◽  
Quantum Markov Semigroup ◽  
Creation Operators

Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation (CAR) in equal-time. In this paper, we consider a quantum Markov semigroup constructed from quantum Bernoulli noises. Among others, we show that the semigroup has infinitely many faithful invariant states that are diagonal, and satisfies the quantum detailed balance condition.

scholarly journals Entropy Production and Detailed Balance for a Class of Quantum Markov Semigroups

2015 ◽  
Vol 22 (03) ◽  
pp. 1550013 ◽  
Author(s):  
F. Fagnola ◽  
R. Rebolledo
Keyword(s):  
Entropy Production ◽  
Weak Coupling ◽  
Detailed Balance ◽  
Weak Coupling Limit ◽  
Invariant State ◽  
Markov Semigroups ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Do So

We give an explicit entropy production formula for a class of quantum Markov semigroups, arising in the weak coupling limit of a system coupled with reservoirs, whose generators [Formula: see text] are sums of other generators [Formula: see text] associated with positive Bohr frequencies [Formula: see text] of the system. As a consequence, we show that any such semigroup satisfies the quantum detailed balance condition with respect to an invariant state if and only if all semigroups generated by each [Formula: see text] do so with respect to the same invariant state.

scholarly journals DYNAMICAL DETAILED BALANCE AND LOCAL KMS CONDITION FOR NON-EQUILIBRIUM STATES

2004 ◽  
Vol 18 (04n05) ◽  
pp. 435-467 ◽  
Author(s):  
LUIGI ACCARDI ◽  
KENTARO IMAFUKU
Keyword(s):  
Transport Coefficients ◽  
Detailed Balance ◽  
Equilibrium States ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Usual Equilibrium ◽  
Kms Condition ◽  
Equivalent Conditions ◽  
Non Equilibrium

The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo–Martin–Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of non-equilibrium quantum systems satisfies a dynamical generalization of the detailed balance condition (dynamical detailed balance) expressing the fact that all the micro-currents, associated to the Bohr frequencies are constant. The usual (equilibrium) detailed balance condition is characterized by the property that this constant is identically zero. From this we deduce a simple and experimentally measurable relation expressing the microcurrent associated to a transition between two levels ∊m→∊n as a linear combination of the occupation probabilities of the two levels, with coefficients given by the generalized susceptivities (transport coefficients). We then give a second characterization of the dynamical detailed balance condition using a master equation rather than the microcurrents. Finally we show that these two conditions are equivalent to a "local" generalization of the usual KMS condition. Summing up: rather than postulating some ansatz on the basis of phenomenological models or of numerical simulations, we deduce, directly in the quantum domain and from fundamental principles, some natural and simple non equilibrium generalizations of the three main characterizations of equilibrium states. Then we prove that these three, apparently very far, conditions are equivalent. These facts support our convinction that these three equivalent conditions capture a universal aspect of non equilibrium phenomena.

THE ASYMMETRIC EXCLUSION QUANTUM MARKOV SEMIGROUP

2009 ◽  
Vol 12 (03) ◽  
pp. 367-385 ◽  
Author(s):  
LEOPOLDO PANTALEÓN-MARTÍNEZ ◽  
ROBERTO QUEZADA
Keyword(s):  
Detailed Balance ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Quantum Processes ◽  
Detailed Balance Condition ◽  
Index Site ◽  
Classical Invariant ◽  
Invariant States ◽  
Quantum Markov Semigroup ◽  
Asymmetric Exclusion

In this paper we study a class of quantum Markov semigroups whose restriction to an abelian sub-algebra coincides, on the configurations with finite support, with the exclusion type semigroups introduced in Liggett's book14 of exchange rates [Formula: see text] not symmetric in the index site r, s. We find a sufficient condition for the existence of infinitely many faithful diagonal (or classical) invariant states for the semigroup, that satisfy a quantum detailed balance condition. This class of semigroups arises naturally in the stochastic limit of quantum interacting particles in the sense of Accardi and Kozyrev.1 We call these semigroups asymmetric exclusion quantum Markov semigroups and the associated processes asymmetric exclusion quantum processes.

scholarly journals GENERATORS OF DETAILED BALANCE QUANTUM MARKOV SEMIGROUPS

2007 ◽  
Vol 10 (03) ◽  
pp. 335-363 ◽  
Author(s):  
FRANCO FAGNOLA ◽  
VERONICA UMANITÀ
Keyword(s):  
Detailed Balance ◽  
Representation Formula ◽  
Markov Semigroup ◽  
Invariant State ◽  
Open Problems ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Adjoint Semigroup ◽  
Quantum Markov Semigroup ◽  
Scalar Products

For a quantum Markov semigroup [Formula: see text] on the algebra [Formula: see text] with a faithful invariant state ρ, we can define an adjoint [Formula: see text] with respect to the scalar product determined by ρ. In this paper, we solve the open problems of characterizing adjoints [Formula: see text] that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators H, Lk in the Gorini–Kossakowski–Sudarshan–Lindblad representation [Formula: see text] of the generator of [Formula: see text]. We study the adjoint semigroup with respect to both scalar products 〈a, b〉 = tr (ρa*b) and 〈a, b〉 = tr (ρ1/2a*ρ1/2 b).

scholarly journals Revisit on the thermodynamic stability of Hořava–Lifshitz black hole

2018 ◽  
Vol 27 (04) ◽  
pp. 1850048
Author(s):  
Xudong Meng ◽  
Ruihong Wang
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Stability ◽  
Detailed Balance ◽  
De Sitter ◽  
Thermodynamic Variable ◽  
Detailed Balance Condition ◽  
First Law Of Thermodynamics ◽  
Balance Condition ◽  
Lifshitz Black Hole

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter [Formula: see text] in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter [Formula: see text] as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

TWO-PHOTON ABSORPTION AND EMISSION PROCESS

2005 ◽  
Vol 08 (04) ◽  
pp. 573-591 ◽  
Author(s):  
FRANCO FAGNOLA ◽  
ROBERTO QUEZADA
Keyword(s):  
Detailed Balance ◽  
Photon Absorption ◽  
Positive Temperature ◽  
Stationary States ◽  
Emission Process ◽  
Absorption And Emission ◽  
Detailed Balance Condition ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Invariant States

We analyze the two-photon absorption and emission process and characterize the stationary states at zero and positive temperature. We show that entangled stationary states exist only at zero temperature and, at positive temperature, there exists infinitely many commuting invariant states satisfying the detailed balance condition.

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