Linear response theory in stochastic many-body systems revisited

Kumiko Hayashi, Shin ichi Sasa

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


The Green-Kubo relation, the Einstein relation, and the fluctuation-response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green-Kubo relation is a direct result of the local detailed balance condition, the fluctuation-response relation represents the dynamic extension of both the Green-Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.

Original languageEnglish
Pages (from-to)407-429
Number of pages23
JournalPhysica A: Statistical Mechanics and its Applications
Issue number2
Publication statusPublished - 2006 Oct 15
Externally publishedYes


  • Driven lattice gas
  • Linear response theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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