In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA spin glass phase can therefore not be valid in any dimension and at any temperature. Further analysis shows that, in general, when systems have many competin...

Ehrenwörtliche Erklärung Ich erkläre, dass ich diese Arbeit selbständig verfasst und keine anderen als die angegebe-nen Quellen und Hilfsmittel benutzt habe.

Most results in multifractal analysis are obtained using either a thermodynamic approach based on existence and uniqueness of equilibrium states or a saturation approach based on some version of the specification property. A general framework incorporating the most important multifractal spectra was introduced by Barreira and Saussol, who used the thermodynamic approach to establish the multifr...

Evolution of non-equilibrium systems towards equilibrium is governed by the second law of thermodynamics. For example, in the previous section we showed that for an adiabatically isolated system entropy must increase in any spontaneous change and reaches a maximum in equilibrium. What about out of equilibrium systems that are not adiabatically isolated and which may also be subject to external ...

This paper focuses on non linear control of non isothermal Continuous Stirred Tank Reactors (CSTRs). The model of the CSTR is thermodynamically consistent in order to apply the control strategy based on the concavity of the entropy function and the use of thermodynamic availability as Lyapunov function. More precisely the stabilization problem of continuous chemical reactors is addressed operat...

In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...

We present an algorithm to evaluate large deviation functions associated to historydependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple time scales, thus extending the work of Giardinà, Kurchan and Peliti [1]. The procedure is supplemented with a thermodynamic-in...