Related papers: Experimentally achieving minimal dissipation via t…
Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost…
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…
According to Landauer's principle, erasure of information is the only part of a computation process that unavoidably involves energy dissipation. If done reversibly, such an erasure generates the minimal heat of $k_BT\ln 2$ per erased bit…
Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…
We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete…
We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous…
Fluid dynamics accompanies with the entropy production thus increases the local temperature, which plays an important role in charged systems such as the ion channel in biological environment and electrodiffusion in capacitors/batteries. In…
We study the thermodynamics of a Brownian particle under the influence of a time multiplexed harmonic potential of finite width. The memory storage mechanism and the erasure protocol realized by time multiplexed potentials are utilized to…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
Recent advances in nonequilibrium statistical physics have provided unprecedented insight into the thermodynamics of dynamic processes. The author recently used these advances to extend Landauer's semi-formal reasoning concerning the…
What are the fundamental limitations for finite-time engines that extract work from active nonequilibrium systems, and what are the optimal protocols that approach them? We show that the finite-time work extraction for nonconservative…
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…
This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). The algorithm is based on a recently introduced variational…
Reducing work fluctuation and dissipation in heat engines or, more generally, information heat engines that perform feedback control is vital to maximize their efficiency. The same problem arises when we attempt to maximize the efficiency…
Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions…
The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently-developed geometric framework for computing optimal protocols for classical systems…
Materials with strongly-correlated electrons exhibit interesting phenomena such as metal-insulator transitions and high-temperature superconductivity. In stark contrast to ordinary metals, electron transport in these materials is thought to…