scholarly journals The stochastic thermodynamics of a rotating Brownian particle in a gradient flow

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Yueheng Lan ◽  
Erik Aurell
Keyword(s):  
Brownian Particle ◽  
Gradient Flow ◽  
Stochastic Thermodynamics

scholarly journals Markov blankets, information geometry and stochastic thermodynamics

2019 ◽  
Vol 378 (2164) ◽  
pp. 20190159 ◽  
Author(s):  
Thomas Parr ◽  
Lancelot Da Costa ◽  
Karl Friston
Keyword(s):  
Gradient Flow ◽  
Information Geometry ◽  
Random Dynamical System ◽  
Stochastic Thermodynamics ◽  
Energy Principle ◽  
Markov Blanket ◽  
Autonomous Computing ◽  
Internal States ◽  
Weakly Mixing ◽  
The Relationship

This paper considers the relationship between thermodynamics, information and inference. In particular, it explores the thermodynamic concomitants of belief updating, under a variational (free energy) principle for self-organization. In brief, any (weakly mixing) random dynamical system that possesses a Markov blanket—i.e. a separation of internal and external states—is equipped with an information geometry. This means that internal states parametrize a probability density over external states. Furthermore, at non-equilibrium steady-state, the flow of internal states can be construed as a gradient flow on a quantity known in statistics as Bayesian model evidence. In short, there is a natural Bayesian mechanics for any system that possesses a Markov blanket. Crucially, this means that there is an explicit link between the inference performed by internal states and their energetics—as characterized by their stochastic thermodynamics. This article is part of the theme issue ‘Harmonizing energy-autonomous computing and intelligence’.

scholarly journals Extracting Work Optimally with Imprecise Measurements

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 8
Author(s):  
Luis Dinis ◽  
Juan Manuel Rodríguez Parrondo
Keyword(s):  
Feedback Loop ◽  
Brownian Particle ◽  
Close Relation ◽  
Optical Tweezer ◽  
Maximum Amount ◽  
Thermal Bath ◽  
Single Measurement ◽  
Stochastic Thermodynamics ◽  
External Agent ◽  
High Degree

Measurement and feedback allows for an external agent to extract work from a system in contact with a single thermal bath. The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information that is acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics. In this paper, we show how to reversibly confine a Brownian particle in an optical tweezer potential and then extract the corresponding increase of the free energy as work. By repeatedly tracking the position of the particle and modifying the potential accordingly, we can extract work optimally, even with a high degree of inaccuracy in the measurements.

Stochastic thermodynamics with a Brownian particle in an optical trap (Presentation Recording)

2015 ◽  
Author(s):  
Ignacio A. Martinez ◽  
Édgar Roldán ◽  
Luis Dinis ◽  
Pau Mestres ◽  
Juan M. R. Parrondo ◽  
...  
Keyword(s):  
Brownian Particle ◽  
Optical Trap ◽  
Stochastic Thermodynamics

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

scholarly journals Genetic recombination as a generalised gradient flow

2021 ◽  
Author(s):  
Frederic Alberti
Keyword(s):  
Arbitrary Number ◽  
Genetic Recombination ◽  
Reaction Network ◽  
Gradient Flow ◽  
Mass Action ◽  
Gradient System ◽  
Gradient Structure ◽  
Law Of Mass Action ◽  
Reversible Chemical Reaction ◽  
Time Partitioning

AbstractIt is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.

scholarly journals Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
James Kohout ◽  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Constant Curvature ◽  
Harmonic Map ◽  
Gradient Flow ◽  
Minimal Immersion ◽  
Curvature Surface ◽  
Previous Theory ◽  
Target Manifold ◽  
Harmonic Map Flow

AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.

scholarly journals Shift a laser beam back and forth to exchange heat and work in thermodynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
John A. C. Albay ◽  
Zhi-Yi Zhou ◽  
Cheng-Hung Chang ◽  
Yonggun Jun
Keyword(s):  
Optical Feedback ◽  
Brownian Particle ◽  
Time Varying ◽  
Optical Technique ◽  
Work Related ◽  
Engine Efficiency ◽  
Confining Potential ◽  
Equipartition Theorem ◽  
Virtual Temperature ◽  
High Flexibility

AbstractAlthough the equivalence of heat and work has been unveiled since Joule’s ingenious experiment in 1845, they rarely originate from the same source in experiments. In this study, we theoretically and experimentally demonstrated how to use a high-precision optical feedback trap to combine the generation of virtual temperature and potential to simultaneously manipulate the heat and work of a small system. This idea was applied to a microscopic Stirling engine consisting of a Brownian particle under a time-varying confining potential and temperature. The experimental results justified the position and the velocity equipartition theorem, confirmed several theoretically predicted energetics, and revealed the engine efficiency as well as its trade-off relation with the output power. The small theory–experiment discrepancy and high flexibility of the swift change of the particle condition highlight the advantage of this optical technique and prove it to be an efficient way for exploring heat and work-related issues in the modern thermodynamics for small systems.

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