Claudia M. Sarris

INFORMATION ENTROPY AND NONLINEAR SEMIQUANTUM DYNAMICS

We describe how, departing from the Shannon entropy, it is possible to deal with semiquantum time-independent nonlinear Hamiltonians. The interplay between the quantal and classical degrees of freedom can be easily seen, and the set of differential equations that govern the temporal evolution of the quantal mean values and the classical variables is obtained. We find invariants of motion and, particularly, we describe under which conditions, the uncertainty principle remains as an invariant of motion too. Through the analysis of these invariants, it is possible to follow the transition of the system from quantum to classical regime and to conclude that the uncertainty principle behaves as an indicator telling us whether the system is in regular or irregular regime. A simple example is shown.

Quantum Decision Making, Legal Complexity and Social Behavior

The relationship between Law (legal system) and Society can be and has been described in many different ways. Beyond the theoretical discussions, there lays reality, and it shows that decisions on legal policies are not neutral in terms of social impact. The legal system is composed by many instruments, institutes or institutions interacting among themselves—laws and other legal norms, including articles within them. It is clear that instruments, institutes or institutions, augment their number according to the appearance of new forms of relationship. Then, the Law is progressively composed by more and more instruments and there is no reason to expect them to be always working in a synchronized way. For this reason Law can be analyzed using complex systems tools, the ‘Legal Complexity Notion’. Moreover, the idea of law is closely related to those of obedience and enforceability. However, a law is not only obeyed just because it is enforceable, but it is considered to express society’s attitude toward a given situation. In other words, people are not likely to perform the behavior described in the law just because it is there. Leaving aside the area of compulsory rules—such as penal law-, where individuals cannot neglect the existence of such a norm, in the vast area of non-compulsory norms—such as contract law-, there are many laws in most legal systems that rule situations that are seldom chosen by the parties of a given business. In the present contribution; we analyze why individuals opt for some legal instruments which are not of compulsory application or do not choose them. One case is the kind of joint venture agreements—contract entailment among enterprises—businessmen decide to enter. Using the available data and a quantum decision-making model, we are able to describe, for the Argentinean case, why among the available typical joint venture regimes, the Temporary Union of Firms—UTE—is preferred by users rather than the Group of Collaborating Firms—ACE—or the Consortium of Cooperating Firms—CCE.

Quantum Dynamics of Non Commutative Algebras: The SU(2) Case

Applying Maximum Entropy Formalism (MEP) the dynamics of Hamiltonians, associated to non commutative Lie algebras, can be found. For the SU(2) case, it is easy to show that the Generalized Uncertainty Principle (GUP) is an invariant of motion. The temporal evolution of the system is confined to Bloch spheres whose radius lay on the interval (0;1). The GUP, defines the fizziness of these spheres inside the \(\hbar\) domain for the SU(2) Lie algebra.

CONSEQUENCES OF THE DYNAMICAL PROPERTIES OF THE SPECIFIC HEAT IN SEMIQUANTUM NONLINEAR HAMILTONIANS

Within the Maximum Entropy Principle context, the specific heat of the system can be expressed in terms of the extensive variables (mean values) or the intensive variables (Lagrange multipliers). It can be shown that the specific heat of the system represented by a given Hamiltonian is not only a thermodynamical quantity but also a dynamical concept. In this contribution, we analyze the consequences emerging from the dynamical properties of the specific heat whose value can be varied using initial conditions independently of the temperature value for the case of semiquantum nonlinear Hamiltonians. An example is outlined.

A General Approach to Describe Nonlinear Semiquantum Motion

We describe a general method to study the nonlinear semiquantum systems: as the dynamics of the system develops in a semiquantum space V spanned by the mean values of a Complete Set of Noncommuting observables (CSNCO) and the conjugate classical variables, X, P, it is possible to define a positive definite metric for the quantum manifold (QM). Through the components of the second rank covariant metric tensor, a close connection between this metric and the uncertainty principle can be established, meanwhile, the classical manifold (CM) of the system, is preserved as a symplectic one. We present an example of an entangled nonlinear semiquantum system where different dynamics take place.