arXiv subjects

Domingos S. P. Salazar

Publications and source records attributed to Domingos S. P. Salazar.

At least 19 recordsLinked to original sources

arXiv2026

Divergence Geometry of Quantum Multi-Mpemba Effects

Two quantum states may relax toward the same steady state, yet the one that starts farther away can overtake the closer one. This is the quantum Mpemba effect. The same pair can reverse order more than once, but these crossings may depend on the divergence used to compare them. We ask which crossings persist for every normalized operator-convex Petz divergence. Because each such divergence is a positive average of one-parameter $χ^2$ kernels, the problem reduces to the sign of one profile across the full kernel range. Alternating sign margins guarantee repeated family-wide reversals, while finite dimension yields a polynomial positivity test. A simple real slow mode fixes the common late-time order; near stationarity, coherence between unequal-eigenvalue sectors makes the order divergence dependent. In a trapped-ion qutrit ideal model, the reported preparation shows divergence-selective crossings. A nearby preparation is a candidate for at least two family-wide reversals.

quant-ph↗

arXiv2026

A minimal qutrit counterexample to Conjecture 4.9 of Lesniewski and Ruskai

Lesniewski and Ruskai conjectured that the contraction coefficient of every monotone Riemannian metric under a unital stochastic map equals the Hilbert--Schmidt contraction on the traceless subspace. We disprove the conjecture with an explicit entanglement-breaking qutrit channel induced by a doubly stochastic $3\times3$ matrix. A faithful diagonal state and a commuting traceless tangent give, simultaneously for every normalized monotone metric, the exact lower bound $η^{\mathrm{Riem}}_κ(Φ_K)\ge 8896/20007>(62+2\sqrt{61})/225=Λ_2(Φ_K^{\dagger}Φ_K)$. The counterexample is entirely classical on a maximal abelian subalgebra. A theorem of Hiai and Ruskai establishes the conjectured identity for all unital qubit maps, so dimension three is minimal among full matrix algebras.

quant-ph↗

arXiv2026

Benign Projective Landscapes for Measured Quantum Divergences

We study nonconvex optimization of measured quantum $f$-divergences over rank-one projective measurements. For smoothly operator-Fenchel liftable generators and faithful states, every projective local maximum and every second-order stationary point is globally optimal over all POVMs. The criterion is blockwise: a critical PVM is optimal exactly when the compressed states are proportional on each equal-score block; otherwise an explicit two-vector rotation has positive ascent curvature. Operator-convex generators admit a positive atomic curvature resolution, and the quadratic $χ^2$ case yields two-sided residual bounds. For binary accessible information, this framework proves the known adaptive-capacity equality and shows that every nonidentical qubit ensemble has exactly two stationary projective measurements, proving conjectures of Keil and Thai--Dall'Arno. A rare-prior limit connects weighted Jensen--Shannon information to relative entropy and yields a finite counterexample to the proposed equivalence between observational-entropy and all-ensemble mutual-information orders. The landscape theorem also covers measured Rényi divergences of finite positive order and measured relative entropy.

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arXiv2026

Bounds for Apparent Second-Law Violations in Quantum Trajectories

Negative stochastic entropy production is commonly called an apparent violation of the second law. In general quantum-trajectory dynamics, however, the physical entropy production $σ$ need not obey a forward detailed fluctuation theorem. A general arbitrary-coupling formulation identifies a dynamical-asymmetry term $σ^\ast$ that completes it into $Ω=σ+σ^\ast$, whose mean is $\langleΩ\rangle=Σ+Σ^\ast$. We prove that the likelihood-ratio sign is optimal among reversal-odd trajectory observables and use this fact to transfer an established sharp fluctuation-theorem floor to the tie-corrected physical sign statistic $Π_σ=\Pr(σ<0)+\Pr(σ=0)/2$. When $\Pr(σ=0)=0$, the result reads $\Pr(σ<0)\ge[1-\langleΩ\rangle/g(\langleΩ\rangle)]/2$, where $g$ is the inverse of $a\mapsto a\tanh(a/2)$. The physical integral fluctuation theorem simultaneously suppresses large negative events, producing a quantitative ``frequent but mild'' law, while the sign imbalance lower-bounds the hidden mean $Σ^\ast$. We formulate the measured-record protocol explicitly and illustrate and numerically audit the tie-corrected theorem in random finite-coupling collision models and a coherently driven qubit interacting with thermal ancillas.

quant-ph↗

arXiv2026

Determinacy Witnesses in the Completely Monotone--Stieltjes--Bernstein Hierarchy

Membership problems in the completely monotone--Stieltjes--Bernstein hierarchy often become explicit after passage to a determinate representation. We organize that passage as a witness calculus. For the Laplace, Stieltjes, and Hausdorff transforms used here, W f denotes the unique admissible signed representing datum; a certificate either proves its positivity or exhibits an obstruction. A concrete dictionary for completely monotone, logarithmically completely monotone, Bernstein, complete Bernstein, and Stieltjes functions and for Hausdorff moment sequences is combined with transport rules for products, shifts, sampling, and Bernstein increments. The applications are consequences of this common calculation. A triple-product identity for a digamma bridge controls ordinary Bernstein and logarithmic complete monotonicity ranges for gamma ratios and gives the strict power cutoff in Szabo's problem. For integer gamma quotients, the inverse Laplace density is a damped Jacobi polynomial, so classical zero geometry decides broad parameter regions. Boundary signs distinguish Bernstein from complete Bernstein behavior and separate completely monotone functions from the Stieltjes class. On the discrete side, signed atoms and finite differences settle interpolation and coefficient questions. The Ramanujan integral and a fractional Volterra symbol provide positive recognition examples. Across the applications, the workflow is the same: normalize the class question, compute or transport its witness, and decide one explicit sign problem. Every exclusion is accompanied by an exact certificate.

math.CA↗

arXiv2026

Riccati Reductions for Modified Bessel Ratios: Bernstein Positivity, Exact Certificates, and Transfer Obstructions

Several open inequalities for ratios and logarithmic derivatives of the modified Bessel functions $I_ν$ of the first kind and $K_ν$ of the second kind reduce to sign questions for quadratic Riccati expressions. We isolate this reduction and use it in two directions. First, for the quotient $W_ν(z)=zI_ν(z)/I_{ν+1}(z)$, the canonical product for $I_{ν+1}$ yields the partial fraction $W_ν(\sqrt{s})=2(ν+1)+2\sum_{n\ge1}s/(s+j_{ν+1,n}^2)$, where $j_{ν+1,n}$ is the $n$-th positive zero of $J_{ν+1}$. Consequently $x\mapsto W_ν(x^τ)$ is a Bernstein function for $ν>-1$ and $0<τ\le1/2$, and this positive exponent range is sharp. Second, an exact rational certificate at $(ν,u)=(0,10)$ places $I_1(10)/I_0(10)$ below 0.949. This refutes the log-concavity question of Baricz, Ponnusamy, and Vuorinen for $u\mapsto \sqrt{u} I_ν(u)$ and its displayed Riccati reformulations. The same framework completes the monotonicity classification of $K_ν'/K_ν^2$, refutes Baricz--Ponnusamy--Vuorinen Question 7 at $ν=1/2$, and gives an entire counterexample to Baricz's coefficient-ratio complete-monotonicity transfer problem.

math.CA↗

arXiv2026

Bernstein Functions at Work: Coalescents, Copulas, and Subordination

Several positivity questions in stochastic processes, dependence modeling, fractional analysis, and renewal theory reduce to a common recognition task: after normalization, identify the object as a Laplace transform, a potential density, an inverse-flow coefficient, or a finite kernel average, and then read the sign pattern from that representation. We develop this recognition calculus for completely monotone functions, Bernstein functions, special Bernstein functions, and probabilistic realizations through subordinators and mixing measures. The main affirmative results settle three narrowly stated source questions in the conventions used by their source papers. Möhle's Problem 6.3 on the block-counting process of exchangeable coalescents with residual singleton mass (dust) is proved by a finite-simplex ordered-pair kernel certificate. For the Pearse--Bondell power-divergence copula generators, we prove complete monotonicity of the inverse throughout the remaining strict negative range $λ\le-1$ identified in their Section 3.8. Together with the special cases already verified in the source paper, this yields Archimedean copulas in every dimension for $λ\le-1$. The Bendikov--Cygan monotonicity question for discrete renewal sequences attached to special Bernstein functions is answered by representing the potential kernel as a Gamma average of a nonincreasing density. Supporting representation and boundary results cover Sibisi's Prabhakar--Pollard $Q$-measure, the Mecke--Nagel--Weiss atom at zero, and the cubic branch criterion $a^2\ge3b$.

math.PR↗

arXiv2026

Strict Total Positivity from Spectral Darboux and Toeplitz Smoothing Mechanisms

We prove two strict total-positivity results by isolating two strictification mechanisms. The first is a spectral Darboux mechanism: an induction converts positivity and ordered endpoint asymptotics for a one-dimensional spectral family into positive Wronskians and hence into strict total positivity. As an application, the modified-Bessel kernel $K(x,s)=I_s(x)$, $x>0$, $s\ge 0$, is strictly totally positive of infinite order. This proves the real-order determinant positivity asked for by Buchstaber and Glutsyuk after their nonnegative-integer-order theorem. The second mechanism is discrete Toeplitz smoothing: every two-sided Polya-frequency sequence is a pointwise limit of totally positive Polya-frequency sequences. This gives a product-topology answer to Question 12.2 of Belton, Guillot, Khare, and Putinar. The density statement is in the product topology on $\mathbb{R}^{\mathbb{Z}}$; no uniform, weighted, or norm-density assertion is made.

math.CA↗

arXiv2026

Order-Moment Transport and Hankel Determinants in Special-Function Inequalities

Scalar inequalities in an order parameter often arise as the $2\times2$ shadow of a stronger Hankel determinant statement. We record a moment-representation criterion: positive exponential and Mellin order representations, together with gamma-normalized completely monotone averages, generate totally nonnegative Hankel kernels, with strictness controlled by the support of the representing measure. The criterion packages the classical total-positivity mechanism as a recognition calculus for special-function inequalities, turning the order parameter into a moment exponent after the correct normalization. The applications include three named determinant lifts. First, we prove the positive Jackson $q$-gamma Hankel conjecture of Karp--Vishnyakova--Zhang: for $0<q<1$, the kernel $(x,y)\mapstoΓ_q(x+y)$ is $\mathrm{STP}_\infty$. This is an atomic Mellin-moment instance of the general criterion; the reciprocal sign-regularity problem for $1/Γ_q$ is separate and is not addressed here. Second, we answer Yang's continuous half-gamma Mills-ratio log-convexity question and strengthen it to strict total positivity, hence to all higher Hankel Turan determinants. Third, we treat Tricomi rays and the one-dimensional Coulomb regularization as all-minor Hankel determinant hierarchies. For the Coulomb regularization, the $2\times2$ minor gives the scalar log-convexity question recorded by Baricz--Pogany, and the full theorem supplies the corresponding all-minor strengthening.

math.CA↗

arXiv2026

Bounded Treewidth and Complete Monotonicity for Scott-Sokal Spanning-Tree Polynomials

Scott and Sokal asked for a structural description of the finite graphs $G$ for which inverse powers $T_G^{-β}$ of the spanning-tree polynomial are completely monotone. We prove the following bounded-treewidth criterion: if $G$ is a finite connected simple graph with $\operatorname{tw}(G)\le k$, then $T_G^{-β}$ is completely monotone for every $β>(k-1)/2$. Consequently, every partial $3$-tree is covered throughout the first Scott--Sokal open interval $1<β<3/2$, including finite Apollonian networks, $K_5-e$, and the four-spoke wheel $W_4$. The proof combines the real Riesz/Wishart integral for determinants, star--mesh elimination of simplicial vertices, and a Gaussian Laplace kernel for the degree-$d$ star. General bounded-treewidth graphs follow by chordal completion and monotone deletion of completion edges.

math.CO↗

arXiv2026

A Bessel-zero obstruction to hyperbolic complete monotonicity of noncentral chi-square densities

Baricz, Prabhu K, Singh and Vijesh asked for the optimal hyperbolically completely monotone (HCM) range of the noncentral chi-square density. The problem was motivated by the gap between known infinite divisibility and the stronger generalized-gamma-convolution/HCM classification. We prove that the HCM range is exactly the central line. More generally, for $a,b>0$ and $θ\ge 0$, the density $p_{a,b,θ}(x)$ is HCM if and only if $θ=0$. Thus the noncentral chi-square density satisfies $χ_{μ,λ}\in\mathrm{HCM}$ if and only if $λ=0$. The proof uses the leading small-$u$ HCM signs of $p(uv)p(u/v)$. These signs are governed by complete Bell polynomials whose signed generating function is $e^{bt}{}_0F_1(;a;-bθt)$. A positive zero inherited from $J_{a-1}$ rules out nonnegative Taylor coefficients when $θ>0$. Consequently, Poisson shape-mixtures of HCM gamma densities need not be HCM.

math.PR↗

arXiv2026

Stable size-biasing and the positive scale-mixture order of generalized Gaussian laws

Let $X_r\sim N_r(0,1)$ be the centered unit-scale generalized Gaussian random variable with density proportional to $\exp(-|x|^r/2)$. We prove that, for $p,q>0$, there exists a strictly positive random variable $V$, independent of $X_q$, such that $X_p\stackrel{d}{=}VX_q$ if and only if $p\le q$. Moreover, the law of $V$ is unique. For $p q$, the required Mellin quotient, viewed as the candidate characteristic function of $\log V$, is unbounded by Stirling's formula, and hence cannot be a characteristic function. The factor laws form a multiplicative cocycle, $V_{p,r}\stackrel{d}{=}V_{p,q}V_{q,r}$, for $p\le q\le r$, where the factors on the right-hand side are independent copies. Thus the Mellin quotient isolated by Dytso, Bustin, Poor and Shamai is realized constructively throughout the $p<q$ branch. In particular, $Φ_{p,q}$ is positive definite exactly in the range $p\le q$, and the inverse Fourier--Mellin candidate density in the remaining $p<q$ branch is a genuine nonnegative probability density. The known Gaussian-base and bounded-parameter product cases are recovered as parts of a single positive scale-mixture classification.

math.PR↗

arXiv2025

Matrix Thermodynamic Uncertainty Relation for Non-Abelian Charge Transport

Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be monitored within a single classical frame. We derive a process-level matrix TUR starting from the operational entropy production $Σ= D(ρ'_{SE}\|ρ'_S\!\otimes\!ρ_E)$. Isolating the experimentally accessible bath divergence $D_{\mathrm{bath}}=D(ρ'_E\|ρ_E)$, we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors $Δq$: $D_{\mathrm{bath}} \ge B(Δq,V,V')$, where the bound depends only on the transported-charge signal $Δq$ and the pre/post collision covariance matrices $V$ and $V'$. In the small-fluctuation regime $D_{\mathrm{bath}}\geq\frac12\,Δq^{\mathsf T}V^{-1}Δq+O(\|Δq\|^4)$, while beyond linear response it remains accurate. Numerical strong-coupling qubit collisions illustrate the bound and demonstrate near-saturation across broad parameter ranges using only local measurements on the bath probe.

quant-ph↗

arXiv2025

Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences

We show that any Petz $f$-divergence (where $f$ is operator convex) between quantum states admits a universal $χ^2$-mixture representation: the distinguishability of $ρ$ from $σ$ is obtained as a positive superposition of quadratic contrasts $χ^2_λ$, with nonnegative weights $w_f(λ)$ determined explicitly from the Stieltjes representation of the generator $f$. This identifies $χ^2_λ$ as atomic building blocks for quantum $f$-divergences and yields closed-form $w_f$ for canonical choices (relative entropy/KL, Hellinger/Bures, R'{e}nyi). By mapping $χ^2_λ$ into a classical Pearson $χ^2$, we leverage the Chapman-Robbins variational representation and obtain a tight and universal quantum thermodynamic uncertainty relation: any $f$-divergence is lower bounded by a function of the statistics of quantum observables (mean and variance), reproducing previous and novel results in quantum thermodynamics as applications.

quant-ph↗

arXiv2024

Thermodynamic uncertainty relation for quantum entropy production

In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum observables, which we will refer to as a thermodynamic uncertainty relation (TUR) for the entropy production. In the absence of coherence between the states, our result reproduces classic TURs in stochastic thermodynamics. For the derivation of the TUR, we introduce a lower bound for a quantum generalization of the $χ^2$ divergence between two states and discuss its implications for stochastic and quantum thermodynamics, as well as the limiting case where it reproduces the quantum Cramér-Rao inequality.

quant-ph↗

arXiv2024

Symmetric Petz-Rényi relative entropy uncertainty relation

Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace norm. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace norm, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics.

quant-ph↗

arXiv2023

Limiting flux in quantum thermodynamics

In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves especially useful near equilibrium. However, this bound tends to be irrelevant in general nonequilibrium situations. We propose a new upper bound for such fluxes in terms of quantum relative entropy, applicable even far from equilibrium and in the strong coupling regime. Additionally, we compare this bound with Monte Carlo simulations of random qubits with coherence, as well as with a model of two interacting nuclear spins.

quant-ph↗

arXiv2023

Quantum relative entropy uncertainty relation

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and non-thermal environments.

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