fluctuation–dissipation theorem

Target entity: fluctuation–dissipation theorem
Context triple: [Einstein–Smoluchowski relation, isSpecialCaseOf, fluctuation–dissipation theorem]

• A. Einstein–Smoluchowski relation
  The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
• B. Fokker–Planck equation
  The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
• C. Feynman–Hellmann theorem
  The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
• D. Langevin dynamics
  Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
• E. Huang–Rhys factor
  The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: fluctuation–dissipation theorem
Target entity description: The fluctuation–dissipation theorem is a fundamental principle in statistical physics that links the random microscopic fluctuations in a system at thermal equilibrium to its macroscopic response to external perturbations.

• A. Einstein–Smoluchowski relation
  The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
• B. Fokker–Planck equation
  The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
• C. Feynman–Hellmann theorem
  The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
• D. Langevin dynamics
  Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
• E. Huang–Rhys factor
  The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
• F. None of above. chosen