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Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the equations governing the optimal control steering \emph{in finite time} the system between two equilibrium states. The…
In thermodynamics one considers thermal systems and the maximization of entropy subject to the conservation of energy. A consequence is Landauer's erasure principle, which states that the erasure of 1 bit of information requires a minimum…
We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical…
Driven barrier crossings are pervasive in optical-trapping experiments and steered molecular-dynamics simulations. Despite the high fidelity of control, the freedom in the choice of driving protocol is rarely exploited to improve…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…
Fluctuation theorems impose fundamental bounds in the statistics of the entropy production, with the second law of thermodynamics being the most famous. Using information theory, we quantify the information of entropy production and find an…
Motivated by the recent proposed models of the information engine [D. Mandal and C. Jarzynski, Proc. Natl. Acad. Sci. 109, 11641 (2012)] and the information refrigerator [D. Mandal, H. T. Quan, and C. Jarzynski, Phys. Rev. Lett. 111, 030602…
Among the emerging technologies with prophesied quantum advantage, quantum communications has already led to fascinating demonstrations -- including quantum teleportation to and from satellites. However, all optical communication…
Landauer discussed the minimum energy necessary for computation and stated that erasure of information is accompanied by heat generation to the amount of kT ln2/bit. Modifying the above statement, we claim that erasure of information is…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Information flow between subsystems is a central concept in information thermodynamics, which provides the second-law-like inequalities for subsystems. This paper discusses the geometric decomposition of information flow, which was…
We focus on the optimization of neutral atom transport and transfer between optical tweezers, both critical steps towards the implementation of quantum processors and simulators. We consider four different types of experimentally relevant…
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a…
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by…
While Landauer's Principle sets a lower bound for the work required for a computation, that work is recoverable for efficient computations. However, practical physical computers, such as modern digital computers or biochemical systems, are…