On the equilibrium state of a small system with random matrix coupling to its environment

J. L. Lebowitz, L. Pastur

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6 Scopus citations


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 HS 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 languageEnglish (US)
Article number265201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number26
StatePublished - 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)


  • Gibbs distribution
  • open systems
  • random matrices

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