Related papers: Optimal Transportation to the Entropy-Power Inequa…
A vast concourse of events and phenomena occur in nature that may be interrelated by a entropy-maximization technique that provides a comprehensible explanation of a range of physical problems, integrating in a new framework the universal…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of…
We introduce an extension of the Optimal Transport problem when multiple costs are involved. Considering each cost as an agent, we aim to share equally between agents the work of transporting one distribution to another. To do so, we…
This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised…
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…
In this paper, we propose our information-theoretic equivalence of entropic multi-marginal optimal transport (MOT). This equivalence can be easily reduced to the case of entropic optimal transport (OT). Because OT is widely used to compare…
Existence of an entropy current with non-negative divergence puts a lot of constraints on the transport coefficients of a fluid, so does the existence of equilibrium. In all the cases we have studied so far we have seen an overlap between…
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed…
*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
We relate transport-entropy inequalities to the study of critical points of functionals defined on the space of probability measures. This approach leads in particular to a new proof of a result by Otto and Villani [43] showing that the…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prekopa-Leindler type…
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
We provide a new proof of the known partial regularity result for the optimal transportation map (Brenier map) between two sets. Contrary to the existing regularity theory for the Monge-Amp{\`e}re equation, which is based on the maximum…
For continuous-space diffusion processes, there is a strong connection between conservative forces and entropy production. For a given time evolution of the system's state, the entropy production is minimized when the system is driven by a…
`Entropy' appears as driving force in many different evolution equations, both deterministic and stochastic, and in these equations this `entropy' also takes different forms. We show how all these examples can be understood as different…