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We show that the $(1+3)$-dimensional `superboost' operators, proposed in Dragan and Ekert's most recent work on superluminal reference frames \cite{Dragan:2022txt}, are simply the canonical Lorentz boosts, expressed in nonstandard notation. Their $(1+3)$-dimensional `superflip', which is claimed to interchange time and space dimensions for a superluminal observer, travelling with infinite speed, is equivalent to applying the identity operator together with an arbitrary relabeling. Physically, it corresponds to staying put within the canonical rest frame, then renaming space as `time' and time as `space'. We conclude that their extension of the `quantum principle of relativity', proposed in earlier work on $(1+1)$-dimensional spacetimes \cite{Dragan:2019grn}, to ordinary Minkowski space \cite{Dragan:2022txt}, is simply Einstein's principle of relativity, proposed in 1905., Comment: Expanded (and hopefully improved). 8 pages, no figures. Comments welcome

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward-backward control system under consistent convex expectation dominated by G-expectation. Under the smooth assumptions for the value function, we get the relationship between MP and DPP under a reference probability by establishing a useful estimate. If the value function is not smooth, then we obtain the first-order sub-jet and super-jet of the value function at any t. However, the processing method in this case is much more difficult than that when t equals 0., Comment: 19 pages

Milgrom's Modified Newtonian Dynamics (MOND) correction to Newtonian gravity is shown to be equivalent to a more fundamental transformation between a non-inertial local reference frame and the fixed background of the observable universe, complying with Mach's principle. Both Newton's gravitational constant and Milgrom's MOND acceleration parameter or scale constant are substituted for the speed of light and two varying and measurable cosmological parameters under the justification of Schr\"odinger's and Sciama's interpretation of Mach's principle: causally connected mass and size of the universe. This Machian interpretation, free from fundamental constants and free parameters with the exception of the speed of light as the speed of causality and gravity, is based on relative field intensities of the small and large scale of the universe. The Machian MOND approximation is a necessary feature of a phenomenological theory of modified inertia which incorporates Mach's principle in agreement with galaxy rotation curves., Comment: 10 pages, published version in International Journal of Theoretical Physics

The exclusivity principle (E-principle) states that the sum of probabilities of pairwise exclusive events cannot exceed 1. Unlike other principles proposed to characterize quantum correlations, its intrinsically non-bipartite formulation enables its application in more general contextuality scenarios. Although equivalent to the no-signalling condition for any bipartite Bell scenario, this equivalence breaks down for two independent copies of the same scenario. Such violations of the E-principle due to multiple copies, known as its activation effect, was studied in [Nat Commun 4, 2263 (2013)] for the nonlocal extremal boxes of $(2,m,2)$, $(2,2,d)$, and $(3,2,2)$ Bell scenarios. The authors mapped the problem of exhibiting activation effects to finding certain cliques inside joint exclusivity graphs. In this work, we refine the joint exclusivity structure to be an edge-colored exclusivity multigraph. This allows us to draw a novel connection to Ramsey theory, which guarantees the existence of certain monochromatic subgraphs in sufficiently large edge-colored cliques, providing a powerful tool for ruling out E-principle violations. We then exploit this connection, drawing on Ramsey-theoretic results to study violations of the E-principle by multiple copies of the contextual extremal boxes of $n$-cycle scenarios, called $n$-cycle PR boxes, for the usual ($n=4$) PR box we show that the known E-principle violation of $5/4$ is the maximal achievable using two copies, and that this same upper bound applies to two copies of the KCBS ($n = 5$) PR box. We then prove that $n \geq 6$-cycle PR boxes, unlike the extremal boxes of the aforementioned Bell scenarios, do not exhibit activation effects with two or three copies. Finally, for any number of independent copies $k$, we establish a lower bound on $n$ above which $n$-cycle PR boxes do not exhibit activation effects with $k$ copies., Comment: 17 pages, 14 figures

The Cosmological Principle is a cornerstone of the standard model of cosmology and shapes how we view the Universe and our place within it. It is imperative, then, to devise multiple observational tests which can identify and quantify possible violations of this foundational principle. One possible method of probing large-scale anisotropies involves the use of weak gravitational lensing. We revisit this approach in order to analyse the imprint of late-time anisotropic expansion on cosmic shear. We show that the cross-correlation of shear $E$- and $B$-modes on large scales can be used to constrain the magnitude (and possibly direction) of anisotropic expansion. We estimate the signal to noise for multipoles $10\lesssim \ell\lesssim 100$ that is achievable by a Euclid-like survey. Our findings suggest that such a survey could detect the $E$-$B$ signal for reasonable values of the late-time anisotropy parameter.

The Landauer principle establishes a lower bound in the amount of energy that should be dissipated in the erasure of one bit of information. The specific value of this dissipated energy is tightly related to the definition of entropy. In this article, we present a generalization of the Landauer principle based on the Tsallis entropy. Some consequences resulting from such a generalization are discussed. These consequences include the modification to the mass ascribed to one bit of information, the generalization of the Landauer principle to the case when the system is embedded in a gravitational field, and the number of bits radiated in the emission of gravitational waves., Comment: 14 pages Latex,1 figure. Invited contribution published in Entropy (SI: The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

Real-time propagation methods for chemistry and physics are invariably formulated using variational techniques. The time-dependent bivariational principle (TD-BIVP) is known to be the proper framework for coupled-cluster type methods, and is here studied from a differential geometric point of view. It is demonstrated how two distinct classical Hamilton's equations of motion arise from considering the real and imaginary parts of the action integral. The latter is new, and can in principle be used to develop novel propagation methods. Conservation laws and Poisson brackets are introduced, completing the analogy with classical mechanics. An overview of established real-time propagation methods is given in the context of our formulation of the TD-BIVP, namely time-dependent traditional coupled-cluster theory, orbital-adaptive coupled-cluster theory, time-dependent orthogonal optimized coupled-cluster theory, and equation-of-motion coupled cluster theory.

The problem of regression extrapolation, or out-of-distribution generalization, arises when predictions are required at test points outside the range of the training data. In such cases, the non-parametric guarantees for regression methods from both statistics and machine learning typically fail. Based on the theory of tail dependence, we propose a novel statistical extrapolation principle. After a suitable, data-adaptive marginal transformation, it assumes a simple relationship between predictors and the response at the boundary of the training predictor samples. This assumption holds for a wide range of models, including non-parametric regression functions with additive noise. Our semi-parametric method, progression, leverages this extrapolation principle and offers guarantees on the approximation error beyond the training data range. We demonstrate how this principle can be effectively integrated with existing approaches, such as random forests and additive models, to improve extrapolation performance on out-of-distribution samples.

This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion (FBM) with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed FBM. To obtain the weak convergence of the controlled systems, we apply the Khasminskii's averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficient of the slow component and the diffusion coefficient of the fast component.

This paper studies the averaging principle of a class of two-time scale stochastic control systems with $\alpha$-stable noise. The associated singular perturbations problem for nonlocal Hamilton-Jacobi-Bellman (HJB) equations is also considered. We construct the effective stochastic control problem and the associated effective HJB equation for the original multiscale stochastic control problem by averaging over the ergodic measure of the fast component. We prove the convergence of the value function using two methods. With the probabilistic method, we show that the value function of the original multiscale stochastic control system converges to the value function of the effective stochastic control system by proving the weak averaging principle of the controlled jump diffusions. Using the PDE method, we study the value function as the viscosity solution of the associated nonlocal HJB equation with singular perturbations. We then prove the convergence using the perturbed test function method.

We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is proved in a Wassersteintype topology, and optimality conditions are written in this abstract setting. This setting encompasses versions of the Schr{\"o}dinger bridge problem with marginal non-linear inequality constraints at every time. In the case of convex constraints, stability results for perturbations both in the constraints and the reference measure are proved. We then specify our results when the reference measure is the path-law of a continuous diffusion process, whose law is constrained at each time. We obtain a complete description of the constrained process through an atypical mean-field PDE system involving a Lagrange multiplier.

Homotopical localizations with respect to (possibly proper) classes of maps are known to exist assuming the validity of a large-cardinal axiom from set theory called Vop\v{e}nka's principle. In this article, we prove that each of the following statements is equivalent to an axiom of lower consistency strength than Vop\v{e}nka's principle, known as weak Vop\v{e}nka's principle: (a) Localization with respect to any class of maps exists in the homotopy category of simplicial sets; (b) Localization with respect to any class of maps exists in the homotopy category of spectra; (c) Localization with respect to any class of morphisms exists in any presentable $\infty$-category; (d) Every full subcategory closed under products and fibres in a triangulated category with locally presentable models is reflective. Our results are established using Wilson's 2020 solution to a long-standing open problem concerning the relative consistency of weak Vop\v{e}nka's principle within the large-cardinal hierarchy., Comment: 30 pages

This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three ways: (1) We reinterpret the classical doubling-of-variables method in the context of second-order equations by casting the Ishii-Crandall Lemma into a test function framework. This adaptation allows us to effectively handle non-local integral operators, such as those associated with L\'evy processes. (2) We translate the key estimate on the difference of Hamiltonians in terms of an adaptation of the probabilistic notion of couplings, providing a unified approach that applies to differential, difference, and integral operators. (3) We strengthen the sup-norm contractivity resulting from the comparison principle to one that encodes continuity in the strict topology. We apply our theory to a variety of examples, in particular, to second-order differential operators and, more generally, generators of spatially inhomogeneous L\'evy processes.