2000/08/31 by Mitsuhiro Kawasaki
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.046145
published as Phys. Rev. E 65, 046145 (2002) (15 pages). · 28 pages(REVTeX), 4 figure(EPS). To be published in Phys. Rev. E
arxiv created 2002/04/04 · openalex publication_date 2002/04/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The experimental time scale dependence of thermodynamic relations in out-of-equilibrium systems with aging phenomena is investigated theoretically by using only aging properties of the two-time correlation functions and the generalized fluctuation-dissipation theorem. We show that there are two experimental time regimes characterized by different thermal properties. In the first regime where the waiting time is much longer than the measurement time, the principle of minimum work holds even though a system is out of equilibrium. In the second regime where both the measurement time and the waiting time are long, the thermal properties are completely different from properties in equilibrium. For the single-correlation-scale systems such as p-spin spherical spin glasses, contrary to a fundamental assumption of thermodynamics, the work done in an infinitely slow operation depends on the path of change of the external field even when the waiting time is infinite. On the other hand, for the multi-correlation-scale systems such as Sherrington-Kirkpatrick model, the work done in an infinitely slow operation is independent of the path. Our results imply that in order to describe thermodynamic properties of systems with aging it is essential to consider the experimental time scales and history of a system as a state variable is necessary.