2008/04/30 by Marcus V. S. Bonança
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Canonical ensemble #Context (archaeology) #Correlation function (quantum field theory) #Dispersion relation #Dissipation #Fluctuation theorem #Fluctuation-dissipation theorem #Limit (mathematics) #Mathematical analysis #Mathematics #Microcanonical ensemble #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical ensemble #Statistical physics #Statistics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.78.031107
published as Phys. Rev. E 78, 031107 (2008) · 15 pages, v3: final version, new text added, new references
openalex publication_date 2008/09/05 · arxiv created 2008/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A derivation of the fluctuation-dissipation theorem for the microcanonical ensemble is presented using linear response theory. The theorem is stated as a relation between the frequency spectra of the symmetric correlation and response functions. When the system is not in the thermodynamic limit, this result can be viewed as an extension of the fluctuation-dissipation relations to a situation where dynamical fluctuations determine the response. Therefore, the relation presented here between equilibrium fluctuations and response can have a very different physical nature from the usual one in the canonical ensemble. These considerations imply that the fluctuation-dissipation theorem is not restricted to the context of the canonical ensemble, where it is usually derived. Dispersion relations and sum rules are also obtained and discussed in the present case. Although analogous to the Kramers-Kronig relations, they are not related to the frequency spectrum but to the energy dependence of the response function.