Optimal control in stochastic thermodynamics

Blaber, Steven; Sivak, David A.

doi:10.1088/2399-6528/acbf04

Cited by 15 publications

(5 citation statements)

References 155 publications

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“…The inequality (12) can be saturated for any control path γ by optimizing its parameterization. To this end, we make the thermodynamic length a functional of a monotonically increasing speed function ϕ t by replacing Λ t with Λ ϕt .…”

Section: Adiabatic Responsementioning

confidence: 99%

“…Thus, any attempt to optimize a given process with respect to its driving protocols generically leads to a complicated dynamical control problem. For systems that are weakly coupled to a thermal environment and driven slowly, relative to their internal relaxation timescale, thermodynamic geometry provides an elegant method to simplify such problems [3][4][5][6][7][8][9][10][11][12][13][14][15]. The key idea of this approach is to solve the equations of motion of the working system, by means of adiabatic perturbation theory [8,16].…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

et al. 2023

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Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose-gas. Our results provide a geometric picture of the BEC-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model [New J. Phys. 24, 025001 (2022)]. Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.

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Section: Adiabatic Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

et al. 2023

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“…The entropy production rate provides a means to quantitatively measure how far from equilibrium a process is, thus elucidating the irreversibility of a process (which produces entropy), the heat produced or work done by the system, or the efficiency of a process [186][187][188][189]. Much recent work has developed optimal control algorithms for non-equilibrium systems to minimize entropy production [102,[190][191][192][193][194][195][196][197][198][199][200][201][202][203]. However, entropy production is frequently difficult to measure in experiments or simulations of complex models, due to the large amount of data needed to reliably estimate probability distributions and currents, although approaches based on machine learning [204][205][206][207][208][209][210] and automatic-differentiation [211] can help.…”

Section: Entropy Production Ratesmentioning

confidence: 99%

Optimization of non-equilibrium self-assembly protocols using Markov state models

Trubiano

Hagan

2022

The Journal of Chemical Physics

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The promise of self-assembly to enable bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite-time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach on two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

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“…Biomimicking the benefits of nonequilibrium drive has attracted great technological interest, with numerous demonstrations such as artificial light-harvesting systems, natural viral capsids, , target-specific delivery of drugs and genes, , formation of supramolecular hydrogels, ,− colloidal diamond photonic crystals, and more. ,,,− Realizing a nonequilibrium self-assembly system would further benefit from control protocols that could assist in navigating the system to the desired target while monitoring its state over time. ,,,− Nevertheless, experimental realizations of these protocols are challenging and require quantitative, coarse-grained observables of the self-assembly process. ,, The time to the first self-assembly can be viewed from the perspective of a mean-first passage time problem, − where control protocols generally aim to reduce the assembly time. Previous works have examined this analogy to study first self-assembly times. − …”

Section: Introductionmentioning

confidence: 99%

“… 10 , 11 , 21 , 58 − 60 Realizing a nonequilibrium self-assembly system would further benefit from control protocols that could assist in navigating the system to the desired target while monitoring its state over time. 23 , 33 , 34 , 61 − 67 Nevertheless, experimental realizations of these protocols are challenging and require quantitative, coarse-grained observables of the self-assembly process. 37 , 62 , 68 The time to the first self-assembly can be viewed from the perspective of a mean-first passage time problem, 69 − 72 where control protocols generally aim to reduce the assembly time.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method

Faran

Bisker

2023

J. Phys. Chem. B

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Many biological systems rely on the ability to self-assemble target structures from different molecular building blocks using nonequilibrium drives, stemming, for example, from chemical potential gradients. The complex interactions between the different components give rise to a rugged energy landscape with a plethora of local minima on the dynamic pathway to the target assembly. Exploring a toy physical model of multicomponents nonequilibrium self-assembly, we demonstrate that a segmented description of the system dynamics can be used to provide predictions of the first assembly times. We show that for a wide range of values of the nonequilibrium drive, a log-normal distribution emerges for the first assembly time statistics. Based on data segmentation by a Bayesian estimator of abrupt changes (BEAST), we further present a general data-based algorithmic scheme, namely, the stochastic landscape method (SLM), for assembly time predictions. We demonstrate that this scheme can be implemented for the first assembly time forecast during a nonequilibrium self-assembly process, with improved prediction power compared to a naïve guess based on the mean remaining time to the first assembly. Our results can be used to establish a general quantitative framework for nonequilibrium systems and to improve control protocols of nonequilibrium self-assembly processes.

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Optimal control in stochastic thermodynamics

Cited by 15 publications

References 155 publications

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Optimization of non-equilibrium self-assembly protocols using Markov state models

Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method

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