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Volumn 65, Issue 4, 2002, Pages

Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation

Author keywords

[No Author keywords available]

Indexed keywords

AGING OF MATERIALS; CORRELATION METHODS; FREE ENERGY; FUNCTIONS; GLASS TRANSITION; PHASE SEPARATION; RELAXATION PROCESSES; SPIN GLASS;

EID: 41349113322     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.046145     Document Type: Article
Times cited : (5)

References (42)
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    • edited by A.P. Young (World Scientific, Singapore), These papers are found also at e-print cond-mat/9607224; and e-print cond-mat/9702070
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    • note
    • It is known that violation of FDT is bounded by the time derivative of the free energy [13]. Since the change of the free energy stops at the long-time limit, FDT holds in the quasi-equilibrium regime even though a system is out of equilibrium.
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    • note
    • 2 does not contribute to the value of the integral by itself.
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    • qsp;1/Δt [19]. Since the correlation function derived from the massless Langevin equation obeys the exponential relaxation, our result agrees with that of Ref. [19].
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    • note
    • This form of the scaling function was proposed to account for the results of experiments in polymer glasses [22], then used in analyses of aging effects in decay of the thermoremanent magnetization [23], and found in the exact solution of the asymmetric spherical SK model [24].
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    • This form of the scaling function is suggested by the numerical data from the analysis of a point particle in a random potential with infinite dimension [26] and is used to scale data for the thermoremanent magnetization and the out-of-phase susceptibility.
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    • 2).
  • 40
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    • note
    • The equations of motion of C(t,t′) and R(t,t′) of the multi-correlation-scale systems in the long waiting time limit have an infinite set of invariance called "time reparametrization invariance" [4]. If we perform an arbitrary reparametrization of time t̂ = ξ(t), t̂′ = ξ(t′) and redefine the two-time quantities as Ĉ(t̂,t̂′) = C[ξ(t),ξ(t′)], Ĝ(t̂,t̂′) = G[ξ(t),ξ(t′)]. Then, the redefined functions Ĉ and Ĝ satisfy the same equations of motion. It is important to note that this invariance is a consequence of having neglected the time derivatives in taking the long waiting time limit The full equations of motion have no such invariance and the solution is unique.


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