Mechanical Proof of the Second Law of Thermodynamics Based on Volume Entropy

In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely mechanical way and suggests that the volume entropy might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of microscopic (quantum or classical) mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law. We discuss how this result relates to the Minimal Work Principle and improves over previous attempts. The natural evolution of entropy is towards larger values because the natural state of matter is at positive temperature. Actually the Law of Entropy Decrease holds in artificially prepared negative temperature systems.Comment: 17 pages, 1 figur

The transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated to the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction and use Lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.Comment: 17 pages, 3 figures, paper submitted tp phys rev

Lifshitz entanglement entropy from holographic cMERA

We study entanglement entropy in free Lifshitz scalar field theories holographically by employing the metrics proposed by Nozaki, Ryu and Takayanagi in \cite{Nozaki:2012zj} obtained from a continuous multi-scale entanglement renormalisation ansatz (cMERA). In these geometries we compute the minimal surface areas governing the entanglement entropy as functions of the dynamical exponent $z$ and we exhibit a transition from an area law to a volume law analytically in the limit of large $z$. We move on to explore the effects of a massive deformation, obtaining results for any $z$ in arbitrary dimension. We then trigger a renormalisation group flow between a Lifshitz theory and a conformal theory and observe a monotonic decrease in entanglement entropy along this flow. We focus on strip regions but also consider a disc in the undeformed theory.Comment: 17 pages, v2: references added and improved discussions, v3: published versio

Raman study of the Verwey transition in Magnetite at high-pressure and low-temperature; effect of Al doping

We report high-pressure low-temperature Raman studies of the Verwey transition in pure and Al-doped magnetite (Fe_3O_4). The low temperature phase of magnetite displays a number of additional Raman modes that serve as transition markers. These transition markers allow one to investigate the effect of hydrostatic pressure on the Verwey transition temperature. Al-doped magnetite Fe_2.8Al_0.2O_4 (TV=116.5K) displays a nearly linear decrease of the transition temperature with an increase of pressure yielding dP/dT_V = -0.096 GPa/K. In contrast pure magnetite displays a significantly steeper slope of the PT equilibrium line with dP/dT_V = -0.18 GPa/K. The slope of the PT equilibrium lines is related to the changes of the molar entropy and molar volume at the transition. We compare our spectroscopic data with that obtained from the ambient pressure specific heat measurements and find a good agreement in the optimally doped magnetite. Our data indicates that Al doping leads to a smaller entropy change and larger volume expansion at the transition. Our data displays the trends that are consistent with the mean field model of the transition that assumes charge ordering in magnetite.Comment: 17 pages, 3 figure