The transition from reversible microdynamics to irreversible transport can be studied very e ciently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to analyze the well-known rate and quantum Boltzmann equations, and present, as a new application, the derivation of a source term which accounts for the spontaneous creation of electron-positron pairs in strong elds. Thereby we emphasize the fundamental importance of time scales: only if the various time scales exhibited by the dynamics are widely disparate, can the evolution of the slower degrees of freedom be described by a conventional Markovian transport equation; otherwise, one must account for nite memory e ects. We show how the projection method can be employed to determine these time scales, and how {if necessary{ it allows one to include memory e ects in a straightforward manner. Finally, there is an appendix in which we discuss the concepts of entropy and macroscopic irreversibility.

A source term in the quantum Boltzrnann equation, which accounts for the spontaneous creation of e+e pairs in external electric fields, is derived from first principles and evaluated numerically. Careful analysis of time scales reveals that this source term is generally non-Markovian. This implies in particular that there may be temporary violations of the H theorem.PACS number(s): 12.38.Mh, 05.70.Ln, 25.75.+r, 52.25. Dg I-INTRODUCTIONThe evolution of the quark-gluon plasma, believed to be formed in the course of relativistic heavy-ion collisions, is commonly described by means of a transport equation [1 -4]. It is well understood how a transport equation can account for acceleration in external Belds, scattering, or (hadro)chemical reactions of the microscopic constituents.There is, however, another physical process which becomes increasingly important at high energies: regions of very large chromoelectric Beld strength may develop and subsequently decay by emitting quarkantiquark pairs [5,6]. This gives rise to the fragmentation of chromoelectric fiux tubes ("strings"), a mechanism frequently invoked to model hadron production [7 -10]. How such spontaneous creation of particles can be incorporated into a transport equation is still not fully understood.Clearly, the transport equation has to be modified by a source term. What is this source term? How can it be derived from the underlying microscopic dynamics?These issues have recently been approached in a Wigner function formulation [11 -15]. But, aside from the fact that it lacks an intuitive probabilistic interpretation, this approach seers &om several practical limitations. The source term cannot be determined completely: it is not known how the longitudinal momenta of the produced particles are distributed. It has been suggested that the distribution is a b function [7]; but while such an ansatz may be useful for practical purposes [13 -15], it is certainly not exact. Furthermore, an interplay of pair creation and collisions, possibly leading to a modification of the source term, has not yet been considered. And Bnally, the Wigner description is not suited for discussing the apparent irreversibility of the particle creation process or the associated generation of entropy. Since pair creation in an external Beld is merely a single-particle problem (see below), the Wigner function retains complete information about the microscopic state of the system. Yet irreversibility never manifests itself on the microscopic level; it only emerges after a suitable coarse graining. I choose a different approach. In collision experiments one usually measures the momentum distribution of the outgoing particles; i.e. , one determines the occupation n+(p, t):= (N+(p))(t) of the various momentum states, with the number operators given by N (p):= ) at(p, m, )a(p, m, ), TYL g N+(p):= ) bt(p, m, )b(p, m, ).mg (Here a and b denote particle and antiparticle field operators, respectively, p the momentum, and m, the spin component. ) This suggests attempting to describe the evolution o...

Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry, probabilities, composition of systems, state preparation and reductionism. The essential distinction between classical and quantum theory, on the other hand, is shown to be joint decidability versus smoothness; for the latter in particular I supply ample explanation and motivation. Finally, I argue that beyond quantum theory there are no other generalisations of classical probability theory that are relevant to physics.Comment: Major revision: key results unchanged, but derivation and discussion completely rewritten; 33 pages, no figure

I show that in tomographic experiments measurement of a small set of observables suffices to confirm or incrementally amend prior expectations with a high degree of confidence. To this end I adapt the evidence procedure, an estimation technique used in classical image reconstruction, to use in quantum state tomography.

I show that quantum theory is the only probabilistic framework that permits arbitrary processes to be emulated by sequences of local measurements. This supports the view that, contrary to conventional wisdom, measurement should not be regarded as a complex phenomenon in need of a dynamical explanation but rather as a primitive-and perhaps the only primitive-operation of the theory.