Related papers: Probability Bracket Notation, Wick-Matsubara Relat…
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability…
The significance of the de Broglie-Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the (orthodox) single-particle Newton-Wigner position. The effect of non-positive excursions of the ensemble…
In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that…
We revisit the localization tensor (LT) from geometric and probabilistic perspectives and construct extensions that are naturally compatible with periodic boundary conditions (PBC), without redefining the position operator. In open boundary…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
In conventional general relativity, the expansion rate H of a Robertson-Walker universe is related to the energy density by the Friedmann equation. Aside from the present day, the only epoch at which we can constrain the expansion history…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
Boltzmann's principleS=k*ln W is generalized to non-equilibrium Hamiltonian systems with possibly fractal distributions in phase space by the box-counting volume. The probabilities P(M) of macroscopic observables M are given by the ratio…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares…
In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…
We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function…
A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical demands (as expected for a "good" measure of entanglement in…
This work presents an effective microscopic, time-dependent Hamiltonian framework for investigating information dynamics during black hole evaporation. While current approaches often rely on gravitational path integrals or statistical…
The thermodynamic binding networks (TBN) model is a tool for studying engineered molecular systems. The TBN model allows one to reason about their behavior through a simplified abstraction that ignores details about molecular composition,…
This work is devoted to the study of the Fokker--Planck equation for a stochastic heat equation with an additive $Q$-Wiener noise and non-homogeneous boundary conditions. We explicitly construct the probability density function and…
Big-bang nucleosynthesis (BBN) is valuable as a means to constrain the physics of the early universe and it is the only probe of the radiation-dominated epoch. A fundamental assumption in BBN is that the nuclear velocity distributions obey…
We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. As a starting point we assume that, for systems initialized in microcanonical states at some energies,…