Quantum thermodynamic Carnot and Otto-like cycles for a two-level system

From the thermodynamic equilibrium properties of a two-level system with variable energy-level gap $\Delta$, and a careful distinction between the Gibbs relation $dE = T dS + (E/\Delta) d\Delta$ and the energy balance equation $dE = \delta Q^\leftarrow - \delta W^\to$, we infer some important aspects of the second law of thermodynamics and, contrary to a recent suggestion based on the analysis of an Otto-like thermodynamic cycle between two values of $\Delta$ of a spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the celebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in principle with no need of an infinite number of infinitesimal processes, provided we cycle smoothly over at least three (in general four) values of $\Delta$, and we change $\Delta$ not only along the isoentropics, but also along the isotherms, e.g., by use of the recently suggested maser-laser tandem technique. We derive general bounds to the net-work to high-temperature-heat ratio for a Carnot cycle and for the 'inscribed' Otto-like cycle, and represent these cycles on useful thermodynamic diagrams.Comment: RevTex4, 4 pages, 1 figur

A variational algorithm for the detection of line segments

In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations outside some approximate edge set, which we represent as the union of a finite number of thin strips, the width of which is an order of magnitude smaller than their length. In order to find a near optimal placement of these strips, we compute an asymptotic expansion of the functional with respect to the strip size. This expansion is then employed for defining a (topological) gradient descent like minimization method. As opposed to a recently proposed method by some of the authors, which uses coverings with balls, the usage of strips includes some directional information into the method, which can be used for obtaining finer edges and can also result in a reduction of computation times

Removing Heat and Conceptual Loops from the Definition of Entropy

A rigorous and general logical scheme is presented, which provides an operative non-statistical definition of entropy valid also in the nonequilibrium domain and free of the usual conceptual loops and unnecessary assumptions that restrict the traditional definition of entropy to the equilibrium domain. The scheme is based on carefully worded operative definitions for all the fundamental concepts employed, including those of system, state of a system, isolated system, separable system, systems uncorrelated form each other, environment of a system, process and reversible process. The treatment considers also systems with movable internal walls and/or semipermeable walls, with chemical reactions and and/or external force fields, and with small numbers of particles. The definition of entropy involves neither the concept of heat nor that of quasistatic process; it applies to both equilibrium and nonequilibrium states. Simple and rigorous proofs of the additivity of entropy and of the principle of entropy nondecrease complete the logical framework

Identifying a space dependent coefficient in a reaction-diffusion equation

We consider a reaction-diffusion equation for the front motion [u] in which the reaction term is given by [c(x)g(u)]. We formulate a suitable inverse problem for the unknowns [u] and [c], where [u] satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [[0,T]]. Uniqueness of the solution is proved in the case of a linear [g]. Assuming [g] non linear, we show uniqueness for large [T]

A nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution

We discuss a nonlinear model for the relaxation by energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels e_i with i=1,2,...,N. The time-dependent occupation probabilities p_i(t) are assumed to obey the nonlinear rate equations tau dp_i/dt=-p_i ln p_i+ alpha(t)p_i-beta(t)e_ip_i where alpha(t) and beta(t) are functionals of the p_i(t)'s that maintain invariant the mean energy E=sum_i e_ip_i(t) and the normalization condition 1=sum_i p_i(t). The entropy S(t)=-k sum_i p_i(t) ln p_i(t) is a non-decreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions p_i(t) of the rate equations are unique and well-defined for arbitrary initial conditions p_i(0) and for all times. Existence and uniqueness both forward and backward in time allows the reconstruction of the primordial lowest entropy state. The time evolution is at all times along the local direction of steepest entropy ascent or, equivalently, of maximal entropy generation. These rate equations have the same mathematical structure and basic features of the nonlinear dynamical equation proposed in a series of papers ended with G.P.Beretta, Found.Phys., 17, 365 (1987) and recently rediscovered in S. Gheorghiu-Svirschevski, Phys.Rev.A, 63, 022105 and 054102 (2001). Numerical results illustrate the features of the dynamics and the differences with the rate equations recently considered for the same problem in M.Lemanska and Z.Jaeger, Physica D, 170, 72 (2002).Comment: 11 pages, 7 eps figures (psfrag use removed), uses subeqn, minor revisions, accepted for Physical Review

Hip Joint Center Localization with an Unscented Kalman Filter

The accurate estimation of the hip joint centre (HJC) in gait analysis and in computer assisted orthopaedic procedures is a basic requirement. Functional methods, based on rigid body localisation, assessing the kinematics of the femur during circumduction movements (pivoting) have been used for estimating the HJC. Localising the femoral segment only, as it is usually done in total knee replacement procedure, can give rise to estimation errors, since the pelvis, during the passive pivoting manoeuvre, might undergo spatial displacements. This paper presents the design and test of an unscented Kalman filter that allows the estimation of the HJC by observing the pose of the femur and the 3D coordinates of a single marker attached to the pelvis. This new approach was validated using a hip joint mechanical simulator, mimicking both hard and soft tissues. The algorithm performances were compared with the literature standards and proved to have better performances in case of pelvis translation greater than 8 mm, thus satisfying the clinical requirements of the application

La comunicazione della patologia fetale. Il punto di vista della donna, del medico e dell’équipe

La comunicazione della patologia fetale riveste una serie di significati con implicazioni psicologiche e sociali importanti che richiedono al medico capacità comunicativa, attitudine alla comprensione della paziente e delle dinamiche istituzionali. La donna: la patologia ostetrica è una crisi dentro la crisi. Nella patologia ostetrica le aspettative di vivere la nuova condizione di madre e di sentirsi più compiutamente famiglia vengono frustrate e tradite. In seguito alla diagnosi di patologia, alla perdita del bambino immaginario può seguire la perdita del bambino reale. Nel caso in cui la coppia decida di proseguire la gravidanza, il sentimento di lutto può prolungarsi per tutta la vita. Il medico: dal momento della prima diagnosi per la donna inizia l’elaborazione del lutto. Anche il medico che comunica la diagnosi vive questo momento con disagio. Inoltre, il medico sente il disagio dell’incertezza: l’incertezza può essere accolta e ascoltata. Raramente in questa situazione è possibile comunicare in modo efficace le informazioni necessarie. È importante comunicare gradualmente e dedicare un secondo incontro alle richieste di spiegazioni. L’équipe: è importante che gli operatori possano condividere questa esperienza all’interno dell’equipe. L’equipe che si occupa di diagnosi prenatale dovrebbe essere composta da persone che hanno scelto liberamente di occuparsi di questo aspetto della medicina. L’equipe diviene un contenitore per le emozioni estreme delle pazienti e degli operatori

Detecting Addiction, Anxiety, and Depression by Users Psychometric Profiles

Detecting and characterizing people with mental disorders is an important task that could help the work of different healthcare professionals. Sometimes, a diagnosis for specific mental disorders requires a long time, possibly causing problems because being diagnosed can give access to support groups, treatment programs, and medications that might help the patients. In this paper, we study the problem of exploiting supervised learning approaches, based on users' psychometric profiles extracted from Reddit posts, to detect users dealing with Addiction, Anxiety, and Depression disorders. The empirical evaluation shows an excellent predictive power of the psychometric profile and that features capturing the post's content are more effective for the classification task than features describing the user writing style. We achieve an accuracy of 96% using the entire psychometric profile and an accuracy of 95% when we exclude from the user profile linguistic features

On the Reconstruction of Cavities in a Nonlinear Model Arising from Cardiac Electrophysiology

In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we propose a new reconstruction algorithm based on Gamma-convergence. The relevance and applicability of this approach are then shown through several numerical experiments