Related papers: Duality, thermodynamics, and the linear programmin…
Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is…
A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…
We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…
Physical analogs have shown considerable promise for understanding the behavior of complex adaptive systems, including macroeconomics, biological systems, social networks, and electric power markets. Many of today's most challenging…
The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on…
We propose a duality between thermodynamics and computational complexity, elevating the difficulty of a computational task to the status of a thermodynamic variable. By introducing a complexity measure C as a novel coordinate, we formulate…
Quantifying the flow of energy within and through fluctuating nanoscale systems poses a significant challenge to understanding microscopic biological machines. A common approach involves coarse-graining, which allows a simplified…
Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling…
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
We consider the thermodynamic approach to the description of economic systems and processes. The first and second laws of thermodynamics as applied to economic systems are derived and analyzed. It is shown that there is a deep analogy…
Shadow molecular dynamics provide an efficient and stable atomistic simulation framework for flexible charge models with long-range electrostatic interactions. While previous implementations have been limited to atomic monopole charge…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We construct a thermodynamic potential that can guide training of a generative model defined on a set of binary degrees of freedom. We argue that upon reduction in description, so as to make the generative model computationally-manageable,…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…
The hypothesis of low entropy in the initial state of the universe usually explains the observed entropy increase is in only one time direction: the thermodynamic arrow of time. The Hamiltonian formalism is commonly used in the context of…
We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a…
Model transformations operate on models conforming to precisely defined metamodels. Consequently, it often seems relatively easy to chain them: the output of a transformation may be given as input to a second one if metamodels match.…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…