A note on the Landauer principle in quantum statistical mechanics

@article{Jaksic2014ANO,
  title={A note on the Landauer principle in quantum statistical mechanics},
  author={Vojkan Jaksic and Claude-Alain Pillet},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={55},
  pages={075210}
}
The Landauer principle asserts 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. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint… Expand
Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle
We study driven finite quantum systems in contact with a thermal reservoir in the regime in which the system changes slowly in comparison to the equilibration time. The associated isothermalExpand
An improved Landauer principle with finite-size corrections
Landauerʼs principle relates entropy decrease and heat dissipation during logically irreversible processes. Most theoretical justifications of Landauerʼs principle either use thermodynamic reasoningExpand
On Landauer’s Principle and Bound for Infinite Systems
  • R. Longo
  • Physics, Computer Science
  • ArXiv
  • 2017
TLDR
This work sets up a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view, and describes a canonical evolution associated with a quantumChannel state transfer by the Tomita–Takesaki modular theory. Expand
Minimising the heat dissipation of information erasure
Quantum state engineering and quantum computation rely on procedures that, up to some fidelity, prepare a quantum object in a pure state. If the object is initially in a statistical mixture, thenExpand
Linear Response Theory and Entropic Fluctuations in Repeated Interaction Quantum Systems
We study Linear Response Theory and Entropic Fluctuations of finite dimensional non-equilibrium repeated interaction systems (RIS). More precisely, in a situation where the temperatures of the probesExpand
Minimising the heat dissipation of quantum information erasure
Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer'sExpand
Adiabatic theorem for closed quantum systems initialized at finite temperature
The evolution of a driven quantum system is said to be adiabatic whenever the state of the system stays close to an instantaneous eigenstate of its time-dependent Hamiltonian. The celebrated quantumExpand
Minimising the heat dissipation of quantum information erasure
Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantumobject in a pure state. Such processes occurwithin LandauerʼsExpand
Finite-bath corrections to the second law of thermodynamics.
TLDR
Finite-bath corrections to the min and max free energies employed in single-shot thermodynamics are derived and it is shown that thermodynamical reversibility is lost in this regime. Expand
Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form
TLDR
By measuring the work required to erase a fraction of a bit of information, the change in entropy is isolated directly, showing that it is compatible with the functional form proposed by Shannon, demonstrating its physical meaning in this context. Expand
...
1
2
...

References

SHOWING 1-10 OF 111 REFERENCES
Thermodynamics of Quantum Information Systems — Hamiltonian Description
TLDR
This work proves the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system, and derives Landauer's principle as a consequence of the second law within the considered model. Expand
Experimental verification of Landauer’s principle linking information and thermodynamics
TLDR
It is established that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles, demonstrating the intimate link between information theory and thermodynamics and highlighting the ultimate physical limit of irreversible computation. Expand
Spectral theory of thermal relaxation
We review some results obtained in a recent series of papers on thermal relaxation in classical and quantum dissipative systems. We consider models where a small system I, with a finite number ofExpand
An improved Landauer principle with finite-size corrections
Landauerʼs principle relates entropy decrease and heat dissipation during logically irreversible processes. Most theoretical justifications of Landauerʼs principle either use thermodynamic reasoningExpand
Entropy production and nonequilibrium stationarity in quantum dynamical systems
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 dissipativeExpand
Topics in nonequilibrium quantum statistical mechanics
These notes are an expanded and revised version of the lectures given by the second and fourth autor in the summer school "Open Quantum System" held in Grenoble, June 16-July 4, 2003. They provide anExpand
Natural Nonequilibrium States in Quantum Statistical Mechanics
A quantum spin system is discussed where a heat flow between infinite reservoirs takes place in a finite region. A time-dependent force may also be acting. Our analysis is based on a simple technicalExpand
On a model for quantum friction III. Ergodic properties of the spin-boson system
We investigate the dynamics of a 2-level atom (or spin 1/2) coupled to a mass-less bosonic field at positive temperature. We prove that, at small coupling, the combined quantum system approachesExpand
On the equilibrium states in quantum statistical mechanics
AbstractRepresentations of theC*-algebra $$\mathfrak{A}$$ of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential μ are studied. Both for finiteExpand
Entropy production in classical and quantum systems
Koopmanism -- the spectral theory of dynamicalsystems -- reduces the study of dynamical properties of a classical or quantum system S to the spectral analysis of its Liouvillean L_S . By definition,Expand
...
1
2
3
4
5
...