Foundational principles of predictive statistical mechanics as the basis for theory of irreversibility

Prediktivna statistička mehanika je oblik zaključivanja iz dostupnih podataka, bez dodatnih pretpostavki, koje nastoji predvidjeti reproducibilne pojave. Primjenom prediktivne statističke mehanike na sustave s Hamiltonovom dinamikom razmotren je problem predviđanja makroskopske vremenske evolucije sustava u slučaju nepotpune informacije o mikroskopskoj dinamici. Cilj istraživanja je analizom temeljnih načela prediktivne statističke mehanike produbiti razumijevanje njene opće primjenjivosti u relaciji s drugim teorijama koje nastoje objasniti pojavu ireverzibilnosti. Osnovna hipoteza je da se to može postići detaljnim razmatranjem uloge koju informacija o sustavu ima u razjašnjenju problema ireverzibilnosti. Hipoteza je provjerena kroz analizu i daljnu generalizaciju rezultata osnovnog teorijskog modela. U modelu zatvorenog Hamiltonovog sustava koji uz Liouvilleovu jednadžbu koristi pojmove teorije informacije analiziran je gubitak korelacije izmedu početnih putanja u faznom prostoru i konačnih mikrostanja, i s tim povezan gubitak informacije o stanju sustava. Primjena načela najveće informacijske entropije maksimizacijom uvjetne informacijske entropije, uz ograničenje koje je dano Liouvilleovom jednadžbom usrednjenom po faznom prostoru, omogućila je definiciju brzine promjene entropije bez dodatnih pretpostavki. Početni model je generaliziran te je uvođenjem dodatnih ograničenja koja su ekvivalentna hidrodinamičkim jednadžbama kontinuiteta doveden u izravnu vezu s poznatim rezultatima iz neravnotežne statističke mehanike i termodinamike ireverzibilnih procesa. Dobiveni rezultati upućuju na općenitu primjenjivost načela prediktivne statističke mehanike i njihovu važnost za teoriju ireverzibilnosti.Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying predictive statistical mechanics to systems with Hamiltonian dynamics, a problem of predicting the macroscopic time evolution of the system in the case of incomplete information about the microscopic dynamics was considered. The goal of the research is to deepen the understanding, through the analysis of the fundamental principles of predictive statistical mechanics, of its general applicability in relation to other theories that seek to explain the phenomenon of irreversibility. Basic hypothesis is that this can be achieved with the detailed consideration of the role that information about the system has in the clarification of the problem of irreversibility. The hypothesis was tested through the analysis and further generalization of the results of the basic theoretical model. In a model of a closed Hamiltonian system that with the Liouville equation uses the concepts of information theory, analysis was conducted of the loss of correlation between the initial phase space paths and final microstates, and of the related loss of information about the state of the system. Applying the principle of maximum information entropy by maximizing the conditional information entropy, subject to the constraint given by the Liouville equation averaged over the phase space, allowed a definition of the rate of change of entropy without additional assumptions. Initial model was generalized, and with the introduction of the additional constraints which are equivalent to the hydrodynamic continuity equations, brought into direct connection with the known results from the nonequilibrium statistical mechanics and thermodynamics of irreversible processes. The results obtained in this work suggest the general applicability of the principles of predictive statistical mechanics and their importance for the theory of irreversibility

Direct Photons from Hot Quark Matter in Renormalized Finite-Time-Path QED

Within the finite-time-path out-of-equilibrium quantum field theory (QFT), we calculate direct photon emission from early stages of heavy ion collisions, from a narrow window, in which uncertainty relations are still important and they provide a new mechanism for production of photons. The basic difference with respect to earlier calculations, leading to diverging results, is that we use renormalized QED of quarks and photons. Our result is a finite contribution that is consistent with uncertainty relations

Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of Theoretical Physic