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We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting…
Irreversible processes accomplished in a fixed time involve nonlinearly coupled flows of matter, energy, and information. Here, using entropy production as an example, we show how thermodynamic uncertainty relations and speed limits on…
We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the $L^2$-Wasserstein…
We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
We establish universal relations between pattern formation and dissipation with a geometric approach to nonequilibrium thermodynamics of deterministic reaction-diffusion systems. We first provide a way to systematically decompose the…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic…
Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
This paper proposes a supervised training algorithm for learning stochastic resource allocation policies with generative diffusion models (GDMs). We formulate the allocation problem as the maximization of an ergodic utility function subject…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…