There is a remarkable interest in the study of out-of-time ordered correlators (OTOCs) that goes from many-body theory and high-energy physics to quantum chaos. In the latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics. The exponential growth has been verified for many paradigmatic maps and systems. However, less is known for multipartite cases. On the other hand, the recently introduced Wigner separability entropy (WSE) and its classical counterpart provide a complexity measure that treats equally quantum and classical distributions in phase space. We compare the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic, double elliptic, and mixed. In all cases, we find that the OTOCs and the WSE have essentially the same behavior, providing a complete characterization in generic bipartite systems and at the same time revealing them as very good measures of quantum complexity for phase-space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Rényi entropy and OTOCs.

We study a generic and paradigmatic two-degrees-of-freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE)-equivalent to the operator space entanglement entropy-and the classical separability entropy (CSE) are used as measures of complexity. For the case where both degrees of freedom are hyperbolic, the maps are classically ergodic and the WSE and the CSE behave similarly, growing to higher values than in the doubly elliptic case. However, when one map is elliptic and the other hyperbolic, the WSE reaches the same asymptotic value than that of the doubly hyperbolic case but at a much slower rate. The CSE only follows the WSE for a few map steps, revealing that classical dynamical features are not enough to explain complexity growth.

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The magnetocaloric effect is the isothermal change of magnetic entropy and the adiabatic temperature change induced in a magnetic material when an external magnetic field is applied. In this work, we present an experimental setup to study this effect in metamagnetic transitions, using the differential thermal analysis technique, which consists in measuring simultaneously the temperatures of the sample of interest and a reference one while an external magnetic field ramp is applied. We have tested our system to measure the magnetocaloric effect in La 0.305 Pr 0.32 Ca 0.375 MnO 3 , which presents phase separation effects at low temperatures (T < 200 K). We obtain ∆T vs H curves, and analyze how the effect varies by changing the rate of the magnetic field ramp. Our results show that the intensity of the effect increases with the magnetic field change rate. We also have obtained the effective heat capacity of the system without the sample by performing calorimetric measurements using a pulse heat method, fitting the temperature change with a two tau description. With this analysis, we are able to describe the influence of the environment and subtract it to calculate the adiabatic temperature change of the sample. Introduction.Since de observation of magnetocaloric effect (MCE) near room temperature in 1997 by Pecharsky et al i an important increase in the amount of work in that topic has been observed. Most of the work has been devoted to obtain a large MCE around room temperature using the most stable, cheapest and easy-to-obtain material. In that sense, materials belonging to different kinds, such as intermetalic compounds, rare earth metals and alloys and manganites were proposed as possible alternatives. But, as the complexity of the systems growths, a more careful interpretation of the relation between the magnetization results and the MCE is needed.