2011/08/29 by Haidong Feng, Jin Wang · 2 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Control and Stability of Dynamical Systems #Curl (programming language) #Curvature #Dissipation #Eigenvalues and eigenvectors #Entropy (arrow of time) #Entropy production #Fluctuation-dissipation theorem #Heat flux #Perturbation (astronomy) #Thermoelastic and Magnetoelastic Phenomena #cond-mat.stat-mech #physics.chem-ph
paper · pdf · doi:10.1063/1.3669448
arxiv created 2011/08/29 · openalex publication_date 2011/12/19 · arxiv updated 2015/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance. The response due to a small perturbation can be expressed by a spontaneous fluctuation. For non-equilibrium systems, we derived a generalized FDT that the response function is composed of two parts: (1) a spontaneous correlation representing the relaxation which is present in the near equilibrium systems with detailed balance and (2) a correlation related to the persistence of the curl flux in steady state, which is also in part linked to a internal curvature of a gauge field. The generalized FDT is also related to the fluctuation theorem. In the equal time limit, the generalized FDT naturally leads to non-equilibrium thermodynamics where the entropy production rate can be decomposed into spontaneous relaxation driven by gradient force and house keeping contribution driven by the non-zero flux that sustains the non-equilibrium environment and breaks the detailed balance. On any particular path, the medium heat dissipation due to the non-zero curl flux is analogous to the Wilson lines of an Abelian gauge theory.