Thermodynamics of the Glassy State

Abstract

Abstract.A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations and the PrigogineDefay ratio.As a second part, the approach connects the response of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized non-equilibrium way. I INTRODUCTIONNon-equilibrium thermodynamics for systems far from equilibrium has long been a field of confusion. A typical application is window glass. Such a system is far from equilibrium: a cubic micron of glass is neither a crystal nor an ordinary undercooled liquid. It is an under-cooled liquid that, in the glass formation process, has fallen out of its meta-stable equilibrium.Until our recent works on this field, the general consensus reached after more than half a century of research was: Thermodynamics does not work for glasses, because there is no equilibrium [1]. This conclusion was mainly based on the failure to understand the Ehrenfest relations and the related Prigogine-Defay ratio. It should be kept in mind that, so far, the approaches leaned very much on equilibrium ideas. Well known examples are the 1951 Davies-Jones paper [2], the 1958 GibbsDiMarzio [3] and the 1965 Adam-Gibbs [4] papers, while a 1981 paper by DiMarzio has title "Equilibrium theory of glasses" and a subtitle "An equilibrium theory of glasses is absolutely necessary" [5]. We shall stress that such approaches are not applicable, due to the inherent non-equilibrium character of the glassy state.Thermodynamics is the most robust field of physics. Its failure to describe the glassy state is quite unsatisfactory, since up to 25 decades in time can be involved. Naively we expect that each decade has its own dynamics, basically independent of the other ones. We have found support for this point in models that can be solved exactly. Thermodynamics then means a description of system properties under smooth enough non-equilibrium conditions.

Understanding quantum measurement from the solution of dynamical models

“…In analogy with what happens in glasses and spin glasses [262,263,264], for physical large times t, the asymptotic value of F dyn (t) is not necessarily the absolute minimum of F(m). It is a weighted average of the free energies of the stable and metastable states, with magnetizations m i .…”

Intrinsic irreversibility of Markovian chains

“…To grasp the impact of our finding, consider, for example, the important debate on the inference of power laws in relaxing systems [18][19][20][21] or in the long tails of probability distributions, which suggests the existence of universal laws underlying many physical phenomena generally associated with complex systems and networks [22][23][24][25]. The basis for these inferences is the comparison of partial, i.e., nonequilibrium, distributions observed up to an experimentally accessible time t to model equilibrium distributions.…”

The formation of glass: a quantitative perspective

“…The glass state below T g is often referred to as the thermodynamic state of a vitrified substance; however, it is still not an equilibrium state [78]. The change in heat capacity at the glass transition, ΔC p , measures the difference between the liquid and solid C p values and can be used to estimate the difference in the Gibbs free energy, ΔG, and other thermodynamic parameters.…”