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Entropy
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Control of Driven Stochastic Systems: From Shortcuts to Optimality
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Control of Driven Stochastic Systems: From Shortcuts to Optimality

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: 15 July 2025 | Viewed by 3188

Special Issue Editors

Dr. Marco Baldovin

E-Mail Website
Guest Editor
CNR—Institute of Complex Systems, 00185 Rome, Italy
Interests: stochastic processes; out-of-equilibrium statistical mechanics; shortcuts to adiabaticity; optimal control; fluctuation–dissipation relation; response theory
Dr. Alessandro Manacorda

E-Mail Website
Guest Editor
Institute for Complex Systems—CNR, 00196 Rome, Italy
Interests: nonequilibrium statistical physics; active matter; glassy dynamics; stochastic processes; optimal control; stochastic resetting
Dr. Dario Lucente

E-Mail Website
Guest Editor
Department of Mathematics & Physics, University of Campania “Luigi Vanvitelli”, 81100 Caserta, Italy
Interests: non-equilibrium statistical mechanics; stochastic thermodynamics; driven stochastic processes; optimal control; machine learning; dynamical systems
Dr. Andrea Plati

E-Mail Website
Guest Editor
Laboratoire de Physique des Solides—CNRS, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
Interests: granular materials (simulations/experiments); driven soft-matter systems; stochastic thermodynamics; optimal control; shortcuts; athermal self-assembly
Prof. Dr. Alessandro Sarracino

E-Mail Website
Guest Editor
Department of Engineering, University of Campania “L. Vanvitelli”, Aversa, CE, Italy
Interests: non-equilibrium statistical mechanics; fluctuation-dissipation relations; granular systems; anomalous diffusion
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, the study of problems related to the control of stochastic dynamics has seen increasing interest. Control theory aims to identify protocols to steer a system to a desired target state in a given time ("shortcuts") or to complete a pre-assigned transition in an optimal way (minimal time, minimal energetic cost). Due to the relentless refinement of experimental techniques, it is now possible to control physical systems subject to different kinds of fluctuations with unprecedented precision, from the nanoscale level (levitated particles, colloids, nanodevices), where thermal fluctuations are not negligible, to the microscopic realm of bacteria and active matter, up to the macroscopic world (vibrated granular materials, energy harvesters). Therefore, the framework of control theory needs to be extended to the stochastic domain, in order to also be applicable to these systems. Besides its implicit applications, this line of investigation has deep connections with fundamental topics in stochastic thermodynamics (efficiency bounds, fluctuations relations) and information theory (Landauer bound).

The goal of this Special Issue is to gather contributions on the different aspects of the subject. We aim, in particular, to present the wide array of approaches that are adopted in this context, such as the use of novel tools in reinforcement learning, alongside well-established analytical methods from control theory.

Dr. Marco Baldovin
Dr. Alessandro Manacorda
Dr. Dario Lucente
Dr. Andrea Plati
Dr. Alessandro Sarracino
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • stochastic processes
  • optimal control
  • shortcuts to adiabaticity
  • nonequilibrium statistical mechanics
  • stochastic thermodynamics
  • dynamic programming
  • reinforcement learning

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Published Papers (4 papers)

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18 pages, 456 KiB  
Article
Optimal Control of an Electromechanical Energy Harvester
by Dario Lucente, Alessandro Manacorda, Andrea Plati, Alessandro Sarracino and Marco Baldovin
Entropy 2025, 27(3), 268; https://doi.org/10.3390/e27030268 - 5 Mar 2025
Viewed by 453
Abstract
Many techniques originally developed in the context of deterministic control theory have recently been applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask what is the best way to change its controllable [...] Read more.
Many techniques originally developed in the context of deterministic control theory have recently been applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask what is the best way to change its controllable parameters in time in order to maximize, on average, a certain reward function, while steering the system between two pre-assigned states. In this work, we study the problem of optimal control for a wide class of stochastic systems, inspired by a model of an energy harvester. The stochastic noise in this system is due to the mechanical vibrations, while the reward function is the average power extracted from them. We consider the case in which the electrical resistance of the harvester can be changed in time, and we exploit the tools of control theory to work out optimal solutions in a perturbative regime, close to the stationary state. Our results show that it is possible to design protocols that perform better than any possible solution with constant resistance. Full article
(This article belongs to the Special Issue Control of Driven Stochastic Systems: From Shortcuts to Optimality)
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34 pages, 2854 KiB  
Article
On the Numerical Integration of the Fokker–Planck Equation Driven by a Mechanical Force and the Bismut–Elworthy–Li Formula
by Julia Sanders and Paolo Muratore-Ginanneschi
Entropy 2025, 27(3), 218; https://doi.org/10.3390/e27030218 - 20 Feb 2025
Cited by 1 | Viewed by 529
Abstract
Optimal control theory aims to find an optimal protocol to steer a system between assigned boundary conditions while minimizing a given cost functional in finite time. Equations arising from these types of problems are often non-linear and difficult to solve numerically. In this [...] Read more.
Optimal control theory aims to find an optimal protocol to steer a system between assigned boundary conditions while minimizing a given cost functional in finite time. Equations arising from these types of problems are often non-linear and difficult to solve numerically. In this article, we describe numerical methods of integration for two partial differential equations that commonly arise in optimal control theory: the Fokker–Planck equation driven by a mechanical potential for which we use the Girsanov theorem; and the Hamilton–Jacobi–Bellman, or dynamic programming, equation for which we find the gradient of its solution using the Bismut–Elworthy–Li formula. The computation of the gradient is necessary to specify the optimal protocol. Finally, we give an example application of the numerical techniques to solving an optimal control problem without spacial discretization using machine learning. Full article
(This article belongs to the Special Issue Control of Driven Stochastic Systems: From Shortcuts to Optimality)
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24 pages, 18984 KiB  
Article
Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle
by Irene Prieto-Rodríguez, Antonio Prados and Carlos A. Plata
Entropy 2025, 27(1), 72; https://doi.org/10.3390/e27010072 - 15 Jan 2025
Viewed by 741
Abstract
Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in [...] Read more.
Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decades allow for expanding the experimental possibilities and designing engines operating with a single particle. In this case, the system of interest cannot be addressed at a macroscopic level and their study is framed in the field of stochastic thermodynamics. In the present work, we study mesoscopic heat engines built with a Brownian particle submitted to harmonic confinement and immersed in a fluid acting as a thermal bath. We design a Stirling-like heat engine, composed of two isothermal and two isochoric branches, by controlling both the stiffness of the harmonic trap and the temperature of the bath. Specifically, we focus on the irreversible, non-quasi-static case—whose finite duration enables the engine to deliver a non-zero output power. This is a crucial aspect, which enables the optimisation of the thermodynamic cycle by maximising the delivered power—thereby addressing a key goal at the practical level. The optimal driving protocols are obtained by using both variational calculus and optimal control theory tools. Furthermore, we numerically explore the dependence of the maximum output power and the corresponding efficiency on the system parameters. Full article
(This article belongs to the Special Issue Control of Driven Stochastic Systems: From Shortcuts to Optimality)
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12 pages, 2085 KiB  
Article
Stochastic Model for a Piezoelectric Energy Harvester Driven by Broadband Vibrations
by Angelo Sanfelice, Luigi Costanzo, Alessandro Lo Schiavo, Alessandro Sarracino and Massimo Vitelli
Entropy 2024, 26(12), 1097; https://doi.org/10.3390/e26121097 - 14 Dec 2024
Cited by 1 | Viewed by 851
Abstract
We present an experimental and numerical study of a piezoelectric energy harvester driven by broadband vibrations. This device can extract power from random fluctuations and can be described by a stochastic model, based on an underdamped Langevin equation with white noise, which mimics [...] Read more.
We present an experimental and numerical study of a piezoelectric energy harvester driven by broadband vibrations. This device can extract power from random fluctuations and can be described by a stochastic model, based on an underdamped Langevin equation with white noise, which mimics the dynamics of the piezoelectric material. A crucial point in the modelisation is represented by the appropriate description of the coupled load circuit that is necessary to harvest electrical energy. We consider a linear load (resistance) and a nonlinear load (diode bridge rectifier connected to the parallel of a capacitance and a load resistance), and focus on the characteristic curve of the extracted power as a function of the load resistance, in order to estimate the optimal values of the parameters that maximise the collected energy. In both cases, we find good agreement between the numerical simulations of the theoretical model and the results obtained in experiments. In particular, we observe a non-monotonic behaviour of the characteristic curve which signals the presence of an optimal value for the load resistance at which the extracted power is maximised. We also address a more theoretical issue, related to the inference of the non-equilibrium features of the system from data: we show that the analysis of high-order correlation functions of the relevant variables, when in the presence of nonlinearities, can represent a simple and effective tool to check the irreversible dynamics. Full article
(This article belongs to the Special Issue Control of Driven Stochastic Systems: From Shortcuts to Optimality)
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