In this article, we proposed a method for describing the evolution of quantum physical systems.We define the action integral on the functional space and the entropy of distribution of observable values on the set of quantum states.Dynamic of quantum system in this article is described as dynamical system represented by one parametric semi group which is extremal of this action integral.Evolution is a chain of change of distribution of observable values.In the closed system, it must increase entropy.Based on the notion of entropy of distribution energy, on the principle of maximum entropy production, we get a picture of evolution of closed quantum systems.
In this article, we proposed a method for describing the evolution of quantum physical systems.We define the action integral on the functional space and the entropy of distribution of observable values on the set of quantum states.Dynamic of quantum system in this article is described as dynamical system represented by one parametric semi group which is extremal of this action integral.Evolution is a chain of change of distribution of observable values.In the closed system, it must increase entropy.Based on the notion of entropy of distribution energy, on the principle of maximum entropy production, we get a picture of evolution of closed quantum systems.
In this article we define and build the one method of description of stochastic evolution of a physical quantum system.For each quantum state U E ω ∈ we construct the probability measure ω µ in the space ( ) , U P S , where U P is the space of the pure states of the quantum system, S the Borel σ -algebra in U P .Farther, for any Hermit's positive element with norm 1 u = , in the C * -algebra of observables U , we define the probability measure u µ on the set of states U E .If strongly conti- nuous group { } t α of * automorphisms on U describes the evolution of struc- ture of observables, according to this, we have a picture of evolution of distribution of states of quantum system relatively to each observable u .
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs’ relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.
The chaos exhibited by a quantum mechanical system is revealed in various aspects such as level spacing, avoiding of level crossing on changing a parameter value, irregular nodal lines of wave function, random matrix and so on. On the other hand since the wave function, the propagator or any physical quantity represented by the average of a phase function is usually quasi-periodic in time development, no exponential divergence of its value takes place between the neighboring two initial values. Furthermore the energy of a kicked oscillator ceases to increase after a certain period of time. These observations lead one to suspect the existence of chaos in quantal systems. It is shown that the nature of quasi-periodicity in quantum system is shared with the distribution function of classical hamiltonian system. The action integral which appears in the formulation of the propagator is the key quantity which can connect the classical and quantal systems, and is considered as serving to search for the origin of quantum chaos. The roles of the action integral in the determination of the energy levels and the behavior of the wave function are discussed.
Abstract The 2nd law of thermodynamics is derived from the principle of least action, positing that the quantum of action is the indivisible and indestructible basic building block of everything. On their least-time paths to balance, the quanta move from the system to its surroundings, or vice versa, so that the kinetic, potential, and dissipated energy tally. When re-expressed in logarithmic terms, this current toward more probable states with decreasing free energy equates to the principle of increasing entropy, the 2nd law of thermodynamics, including path-independent dynamic and path dependent geometric phase shifts. Despite being exact, the equation of evolution to entropy maximum, equivalent to free energy minimum, cannot be solved because evolution, consuming its own driving forces, becomes path dependent. Thus, the future remains open within free energy bounds. As discussed, the entropy derived from the statistical physics of open quantum systems sums states distinguishable in energy; whereas, Boltzmann’s entropy enumerates microstates indistinguishable in energy. Consequently, the statistical physics of open systems differs from that of closed systems: The irreversible evolution in the state space toward thermodynamic balance contrasts with the steady-state revolution in phase space between conceivable configurations. This concrete comprehension explains, among other things, that increasing disorder is not a law of nature itself but a consequence of the law to attain balance with incoherent surroundings in the least time.
The problem of constructing models for the statistical dynamics of finite-level quantum mechanical systems is considered. The maximum entropy principle formulated by E.T. Jaynes in 1957 and asserting that the entropy of any physical system increases until it attains its maximum value under constraints imposed by other physical laws is applied. In accordance with this principle, the von Neumann entropy is taken for the objective function; a dynamical equation describing the evolution of the density operator in finite-level systems is derived by using the speed gradient principle. In this case, physical constraints are the mass conservation law and the energy conservation law. The stability of the equilibrium points of the system thus obtained is investigated. By using LaSalle’s theorem, it is shown that the density function tends to a Gibbs distribution, under which the entropy attains its maximum. The method is exemplified by analyzing a finite system of identical particles distributed between cells. Results of numerical simulation are presented.
Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.