# The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics

@article{Jaksic2006TheGF, title={The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics}, author={Vojkan Jaksic and Yoshiko Ogata and Claude-Alain Pillet}, journal={Communications in Mathematical Physics}, year={2006}, volume={265}, pages={721-738} }

We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.

## 57 Citations

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## References

SHOWING 1-10 OF 54 REFERENCES

### Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

- Physics
- 2002

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in refs. 1–7. In the algebraic formalism of quantum statistical mechanics we…

### Theory of quantum fluctuations and the Onsager relations

- Physics
- 1989

A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to…

### Linear Response Theory for Thermally Driven Quantum Open Systems

- Physics
- 2006

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys.…

### Transport properties of quasi-free fermions

- Physics
- 2007

Using the scattering approach to the construction of Non-Equilibrium Steady States proposed by Ruelle we study the transport properties of systems of independent electrons. We show that…

### On Entropy Production in Quantum Statistical Mechanics

- Physics
- 2001

Abstract: We propose a definition of entropy production in the framework of algebraic quantum statistical mechanics. We relate our definition to heat flows through the system. We also prove that…

### About the exactness of the linear response theory

- Mathematics
- 1991

For quantum lattice systems with finite range potentials and integrable space clustering, we prove the linearity of the response theory when dealing with fluctuation observables.

### Topics in quantum statistical mechanics and operator algebras

- Physics
- 2001

The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to…

### The Green-Kubo Formula for the Spin-Fermion System

- Physics
- 2006

AbstractThe spin-fermion model describes a two level quantum system
$$\mathcal{S}$$ (spin 1/2) coupled to finitely many free Fermi gas reservoirs
$$\mathcal{R}_{j}$$ which are in thermal equilibrium…

### Natural Nonequilibrium States in Quantum Statistical Mechanics

- Physics
- 1999

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 technical…