Related papers: Nonequilibrium statistical operator method in the …
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
We provide a unifying axiomatics for Renyi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszar's measure of directed divergence known from communication theory.
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established.…
The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schr\"odinger equation is also given. The dissipative and stochastic propagators are linked by the…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
The maximum entropy technique (MENT) is used to determine the distribution functions of physical values. MENT naturally combines required maximum entropy, the properties of a system and connection conditions in the form of restrictions…
This chapter seeks to outline a few basic problems in quantum statistical physics where recent experimental advances from the atomic physics community offer the hope of dramatic progress. The focus is on nonequilibrium situations where the…
We suggest a certain statistical interpretation for the entropy produced in driven thermodynamic processes. The exponential function of half irreversible entropy re-weights the probability of the standard Ornstein-Uhlenbeck-type…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered. The relativistic mass distribution for…
R\'enyi transfer entropy (RTE) is a generalization of classical transfer entropy that replaces Shannon's entropy with R\'enyi's information measure. This, in turn, introduces a new tunable parameter $\alpha$, which accounts for sensitivity…
The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum…
Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium…
For the system with inhomogeneous distribution of macroscopic parameters we obtain thermodynamic relation which depends on the spatial point (coordinate). In our approach, to obtain such a relation we use the basic ideas of the method of…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
Closely related to the laws of thermodynamics, the detection and quantification of disequilibria are crucial in unraveling the complexities of nature, particularly those beneath observable layers. Theoretical developments in nonequilibrium…
Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…