The Discrete-Continuous Logic and its possible quantum realizations

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate that on the set of propositions of this kind one can define both the discrete logical operations (connectives) such as negation and strong logical disjunction and in addition one parameter group of continuous operations (logical rotations). We prove that an arbitrary classical proposition (which in this logic is represented by the purely diagonal matrix) can be considered as the result of strong disjunction of two identical GP. This fact gives one a good reason to presume the DCL as a prime logical substructure underlying to ordinary propositional logic, which is recorded by our consciousness. We believe that proposed version of DCL will find many applications both in physics (quantum logic) and also in cognitive sciences (mental imagery) for better understanding of the pecular nature of mental brain operations.Comment: 6 pages, no figure

Quasithermodynamic Representation of the Pauli Markov equation and their possible applications

We demonstrate that the extensive class of open Markov quantum systems describing by the Pauli master equation can be represented in so- called quasithermodynamic form .Such representation has certain advantages in many respects for example it allows one to specify precisely the parameter region in which the relaxation of the system in question to its stationary state occurs monotonically.With a view to illustrate possible applications of such representation we consider concrete Markov model that has in our opinion self-dependent interest namely the explanation of important and well established by numerous experiments the Yerkes-Dodson law in psychologyComment: 5 page

The Characteristic Noise Induced by the Continious Measurements in Classical Open Systems

We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is described by the Fokker-Planck equation of a special form. The diffusion tensor of this equation is uniquely defined by a type of the measured quantity. On the basis of the approach proposed the stationary states of the linear dissipative systems, induced by measurements in them, are considered. Also we demonstrate on the simple example, how in the conservative system, consisting of noninteracting parts, measurement of the integral of motion results in relaxation to the quasi-thermodynamic equilibrium between parts of the system. The "temperature" of such state is determined by energy of the system and by the mean value of measured integral of motion. PACS numbers: 03.65.Ta, 05.40.-aComment: 13 p., 0 fi

Quasithermodynamic Representation of the quantum master equations: its existence , advantages and applications

We propose a new representation for several quantum master equations in so-called quasithermodynamic form. This representation (when it exists) let one to write down dynamical equations both for diagonal and non-diagonal elements of density matrix of the quantum system of interest in unified form by means of nonequilibrium potential ("entropy") that is a certain quadratic function depending on all variables describing the state. We prove that above representation exists for the general Pauli master equation and for the Lindblad master equation ( at least in simple cases ) as well. We discuss also advantages of the representation proposed in the study of kinetic properties of open quantum systems particularly of its relaxation to the stationary state.Comment: 6 page

Quantum Look at two Common Logics: the Logic of Primitive Thinking and the Logic of Everyday Human Reasoning

Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive (mythological) thinking and the second one as the toy model of everyday human reasoning in which aside from logical deduction, heuristic elements and beliefs also play the considerable role. Several arguments in favor of the interpretations proposed are adduced and discussed in the paper as well.Comment: 7 page

The connection between phase synchronization in simple nonlinear system and stationary state entanglement in its quantum counterpart

We begin with the simple model of phase sychronization in open classical nonlinear system which is represented in the language of angular momentum variables. After that we propose the relevant quantum counterpart of this system. Using the appropriate Lindblad master equation for the density matrix of two qubit realization of such system we have revealed that stationary state of this composite system is pure and entangled with small dispersion of phase observable. We believe that such curious connection between entangled stationary states of quantum composite system and phase sychronization between its subsystems may be typical for rather wide class of similar nonlinear open systems as well.Comment: 4 page

Unified Statistical Description of Quasithermodynamic Systems in and out of Equilibrium

We propose the method of statistical description of broad class of dynamic systems (DS) whose equations of motion are determined by two state depending functions: 1) "energy" - the quantity which conserves in time and 2) "entropy" - the quantity which does not decrease in time. It is demonstrated that the behavior of such systems in the equilibrium state reduces to the thermodynamic lows in particular the Le Chatelier principle is satisfed and so on. Taking into account the interaction system of interest with ergometer - the device which continuously measures its energy one can possible to find the system distribution function in arbitrary non-equilibrium stationary state (NESS). Some general relations for mean values of certain quantities in NESS which can be compared with experimental data are obtained.Comment: 11 page

Three "quantum" models of competition and cooperation in interacting biological populations and social groups

In present paper we propose the consistent statistical approach which appropriate for a number of models describing both behavior of biological populations and various social groups interacting with each other.The approach proposed based on the ideas of quantum theory of open systems (QTOS) and allows one to account explicitly both discreteness of a system variables and their fluctuations near mean values.Therefore this approach can be applied also for the description of small populations where standard dynamical methods are failed. We study in detail three typical models of interaction between populations and groups: 1) antagonistic struggle between two populations 2) cooperation (or, more precisely, obligatory mutualism) between two species 3) the formation of coalition between two feeble groups in their conflict with third one that is more powerful . The models considered in a sense are mutually complementary and include the most types of interaction between populations and groups. Besides this method can be generalized on the case of more complex models in statistical physics and also in ecology, sociology and other "soft' sciences.Comment: 8 pages, 0 figure

On the relationship between quantum entanglement and classical synchronization in open systems

We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional Hilbert space. The analysis of the simplest two qubit version of the quantum model shows that all its stationary states are nonseparable.Comment: 7 page

The quantum approach to human reasoning does explain the belief-bias effect

Based on the ideas of quantum physics and dual-process theory of human reasoning that takes into account two primary mechanisms of reasoning : 1) deductive rational thinking and 2) intuitive heuristic judgment, we proposed the "quantum" approach to practical human logic that allows one to specify the most distinctive peculiarities in activity of two reasoning systems mentioned above and in addition to describe phenomenologically well-established experimentally belief-bias effect