Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: Curvature, gauge field, and generalized fluctuation-dissipation theorem

Journal Article · Wed Dec 21 04:00:00 EST 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3669448· OSTI ID:22038810

Haidong, Feng ^[1]; Jin, Wang ^[1]

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1. Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States)

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.

• OSTI ID: 22038810
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 23 Vol. 135; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DECOMPOSITION
ENTROPY
FLUCTUATIONS
GAUGE INVARIANCE
PERTURBATION THEORY
QUANTUM FIELD THEORY
RELAXATION
RESPONSE FUNCTIONS
THERMODYNAMICS