### Abstract

We consider a random matrix model of interaction between a small n-level system, S, and its environment, a N-level heat reservoir, R. The interaction between S and R is modeled by a tensor product of a fixed matrix and a Hermitian random matrix. We show that under certain 'macroscopicity' conditions on R, the reduced density matrix of the system , is given by , where H_{S} is the Hamiltonian of the isolated system. This holds for all strengths of the interaction and thus gives some justification for using to describe some nano-systems, like biopolymers, in equilibrium with their environment (Seifert 2012 Rep. Prog. Phys. 75 126001). Our results extend those obtained previously in (Lebowitz and Pastur 2004 J. Phys. A: Math. Gen. 37 1517-34); (Lebowitz et al 2007 Contemporary Mathematics (Providence RI: American Mathematical Society) pp 199-218) for a special two-level system.

Original language | English (US) |
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Article number | 265201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 26 |

DOIs | |

State | Published - Jul 3 2015 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Keywords

- Gibbs distribution
- open systems
- random matrices