The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case to the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is just the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the Hilbert space version of the mathematics of partitions. Or putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic to information theory to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partitions are the ordered pairs of elements from the underlying set that are in different blocks of the partition. Logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run through the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives).

A well known result for the interference of two single-mode fields is that the degree of coherence and the degree of indistinguishablity are same when we consider the detection of a single photon. In this article we present the relation between degree of coherence, path indistinguishability and the fringe visibility considering interference of multiple number of single-mode fields while being interested in the detection of a single photon only . We will also mention how Born’s rule of interference for multiple sources is reflected in these results.

Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in quantum mechanics the standard view is that particles of the same kind (``identical particles'') are completely indistinguishable from each other. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of ``particle'' in ordinary language and in classical physical theory, but also with how this term is used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by ``particles'' in the classical limit of quantum mechanics. Elaborating on earlier work, we here discuss an alternative to the standard view that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information theory concerning the question of when identical particles can be considered to be entangled.

Quantum theory is the land of indiscernible things, of things that in some situations cannot be put apart. This contrasts in much with standard mathematics and classical logic, which were elaborated to deal with \textit{individuals}, discernible things. Many thinkers, among them the mathematician Yuri Manin, have proposed that a more general theory of `sets' than standard set theories (where sets are collections of discernible elements) should be elaborated to cope with quantum physics. Quasi-set theory was proposed with such an aim. In this paper, we consider some aspects of this theory and discuss the way we can use such a theory as a framework for constructing deformable (not rigid) structures where indiscernible things can be considered but with one additional and fundamental detail: these structures cannot be extended to rigid structures as it happens in the standard frameworks. Really, the way of dealing with indiscernible (or indistinguishable) elements within a `standard' framework such as a `classical' set theory (like the ZFC system) requires the confinement of the discussion to deformable (non-rigid) structures. But in ZFC every structure can be extended to a rigid structure (encompassing only the trivial automorphism -- the identity function), so that in the extended structure (or in the whole universe) one can realize that the supposed indiscernible objects are not indiscernible at all. Quasi-set theory is such that the universe of quasi-sets is deformable and in such a theory one can construct deformable structures which cannot be extended to rigid ones. The aim of this paper is to put these things in a clear way.

This is a review on social laser theory completed with its new developments and applications. An important methodological step towards similarity with quantum physics is the invention and consistent operation with infons. These are excitations of the quantum social-information field carrying social energy and coarse grained content of communications (their color and quasi-color). We study in more detail interactions of infons with social atoms, the processes of absorption and emission (spontaneous and stimulated). We also analyze the dynamics of iterations of the cascades of infons in the social resonators. The latter are based on social networks coupled to laser's gain medium composed of social atoms. Consideration of the pro-war and pro-peace beams leads to the general discussion on the competing beams of social radiation and the conditions for their creation and coexistence. The role of social networks in lasing is illustrated by the protests during the COVID-19 pandemic. It is highlighted that a human gain medium can approach the state of population inversion with supply of infons of one sort (quasi-color), but the stimulated emission can be induced by injection into the gain medium of infons of a different quasi-color. We call this behavior of social atoms memorylessness. This theoretical property is illustrated with the examples from the modern social-political life.

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature. The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation. The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts. Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society. Application of the quantum-like model of Frhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and internet based sources.