The revealed integral energy shows the vortex nature of quantum realm

ing of the evolution, the state of ρ at any given instant t = ti can be taken for ideally entrained by fitting. Due to this and since ρ is assumed smooth in t, the effect of the irreducibility of I and [H, ρ] to invariants is weak for t’s close to ti. So, it may seem reasonable to judge about their figure of merit for not small t − ti by popular perturbation methods of dynamical systems, e.g. [8]. But this insight is insufficient and fails in the long run beyond the domain of ideal to match the future with the past. As the relience on such perturbation theories conforms to the trends of ρ in line with a dressed Hamiltonian, it conduces to the belief in this energy function theory beyond its above-established rigid constraints. By virtue of the considered canonical feature the system’s behavior in externally applied fields changes generally in a non-conservative way. It shows up vigorously in systems under fields of high frequences, particularly near resonances, including parametric and combinational. The averaged effect of hf fields in the lowest, quadratic order in field amplitude results in static vortex forces along with strong forces of effective potential. Thereat, the quasi-steady states, fluctuations and stability of systems at resonances appear quite different from what the theories of quasi-energy and generalized thermodynamic potential prescribe. Various essential effects of this kind, their general features and methods of analysis were elucidated in our work cited in [5a]. The extended equilibrium and measurements In the above, along with the new notion of energy we have come to a new notion of equilibrium states – the extention of habitual stereotype of system states of rest to the equilibrium states of motion that take place in an immencely wider area of conditions. The conclusion is immediate from the equations (5) describing generally irreversible kinetics with ∂ρ/∂t 6= 0 and allows for the states of fast motion. However, it relates to the nonequilibrium statistical physics associated with an irreversible transfer of energy rather as a contraposition, for the matter concerns the physics of systems in equilibrium states in outer stationary conditions when the energy is conserved. Is there then a derogation from stationarity? The question is not so academic as principal for the measurements and understanding of the claimed principles. The stationarity for the case is the invariance of behaviors with respect to time translation from the time of perturbation, and it is inherent as in the states of rest as in the states of steady motion. The difference between the two displays itself in comparing the temporal correlations between the pictures of steady distributions of ρ for the system. Just determining these correlations or the power spectra corresponding to them for these or those forms of motion gives one the approach to the phenomena in point, including the region of rest-motion transition. Generally, the approach within the framework of Eq. (9) does not give one the entire range of desired correlations, for it governs the trends already smoothed over frequently alternating influences on the system, hence, generally insufficient for descriptions of all correlations of system states at different moments of time. The latter are described by more detailed kinetics and energy measures. We shall not dwell on that here. For the systems relaxing in stationary outer conditions to equilibrium distributions of states close to the states of rest, in the sense of limit ∂ρ/∂t → 0, we get in terms of Eq. (9) [H, ρ] + I = 0. (12) The energy of systems is then conserved with the branch I acting on a par with [H, ρ] in jointly keeping the circulation and transformations of conserved energy. To similar trends we come for the energy of stable equilibrium states of fast motion in the picture of canonical transformations where the steady ρ is roughly t-independent. It is clear that the conditions of such energy circulation and transformations in systems include the whole domain of ideal, but are not limited by it at all and can stretch beyond the ideal vastly. Whereas in the domain of ideal (whether Eq. (12) holds or not) the energy is a function of system states given by a dressed Hamiltonian with its potential and kinetic energy, both of regular and chaotic origin, the conserved energy of systems beyond the ideal includes or comprises the energy of a different form, complementary to all those types given by Hamiltonian functions, for it represents both the reversible and irreversible drift forces and diffusion in their integral inseparable balance. This is just the integral vortex energy of equilibrium states in systems. It is not related to the principles of detailed balance and habitual trends of relaxation, which is to the minimum of energy as a function of system states, hence, the trends of stability and preference relations in phase transitions all that given by the traditional theory of phase transitions and other phenomena based on the theory of generalized thermodynamic potential. On the macromotion and vortex energy criteria Look first at a Brownian particle on a reflecting plate. Gravity tends to press the particle down and chaotic influences of the environment keep it hopping on the plate in stationary conditions. For the particle charged and placed in a field of a permanent magnet, its drift arises across both the magnetic and gravity force fields. The drift modifies but not disappears for the plate rolled into a closed pipe or box. The energy of steady drift is conserved, hence, contains a vortex form not given by a function of the system states. The same is for a number