Related papers: The Architecture of Inter-Level Representation
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
Living systems are maintained out-of-equilibrium by external driving forces. At stationarity, they exhibit emergent selection phenomena that break equilibrium symmetries and originate from the expansion of the accessible chemical space due…
We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
A model is proposed for studying the reaction dynamics in complex quantum systems in which the complete mixing of states is hindered by an internal barrier. Such systems are often treated by the transition-state theory, also known in…
Recently many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
Social network extensions of Heider's balance theory have not always been consistent. Structural balance theory primarily focuses on graph partitioning, thereby assuming, homogeneity in balance-driven behavior of nodes. We present a general…
Recently, it has been argued that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics. Here, under a different free choice…
We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical…
Stochastic and dynamical processes lie at the heart of all physical, chemical, and biological systems. However, kinetic and thermodynamic properties which characterize these processes have largely been treated separately as they can be…
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is…
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…