Stochastic Thermodynamics: A Dynamical Systems Approach

Rajpurohit, Tanmay; Haddad, Wassim M.

doi:10.3390/e19120693

Cited by 10 publications

(5 citation statements)

References 51 publications

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“…The present work follows a long line of contributions within the control field to draw links between thermodynamics and control, see e.g., [6], [28], [25], [31], [30], [39]. More recently, important insights have linked the Wasserstein distance of optimal mass transport, which itself is a solution to a stochastic control problem, to the dissipation mechanism in stochastic thermodynamics [3], [2], [34], [13], [17].…”

Section: Discussionmentioning

confidence: 99%

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Maximal power output of a stochastic thermodynamic engine

Taghvaei

Chen

et al. 2020

Preprint

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Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines, by bounding the maximal amount of mechanical energy produced, compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasistatic processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Indeed, the problem to optimize power can be expressed as a stochastic control problem. Building on this framework of stochastic thermodynamics we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (Tc cold, and T h hot). Specifically, assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by M 8 ( T h Tc − 1). Moreover, we show that this bound can be reached to within a factor of ( T h Tc − 1)/( T h Tc + 1) by operating the cyclic thermodynamic process with a quadratic potential.

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Section: Discussionmentioning

confidence: 99%

“…Consider the expression in (30) for the power that can be drawn via a cyclic operation as discussed. Preparation of the ensemble, and actuation during the cycle, allow a number of choices.…”

Section: Fundamental Limits To Powermentioning

confidence: 99%

Maximal power output of a stochastic thermodynamic engine

Taghvaei

Chen

et al. 2020

Preprint

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“…This constraint implies that the ith subsystem cannot supply any energy to the other subsystems or the environment, dissipate energy to the environment, nor be subject to stochastic energy fluctuations whenever its internal energy is zero. In this case, it can be shown that the resulting dynamical system is a non-negative dynamical system [12,30], and hence, scriptD=Rfalse¯+n, where Rfalse¯+n denotes the non-negative orthant of Rn. The input space U is assumed to be U=Rn.…”

Section: Stochastic Thermodynamic Modelmentioning

confidence: 99%

“…Damping (i.e. deceleration) of the system particles due to frictional effects leading to local heating of the fluid and resulting in entropy production, and the energy addition of the particles due to thermal fluctuations leading to local cooling of the fluid and resulting in entropy consumption, is evaluated using fluctuation theorems (see [12,13] and the numerous references therein). Thus, even though for stochastic thermodynamic models, the average entropy is positive (i.e.…”

Section: Introductionmentioning

confidence: 99%

Stochastic thermodynamics: dissipativity, accumulativity, energy storage and entropy production

Lanchares

Haddad

2023

Phil. Trans. R. Soc. A.

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In this paper, we develop an energy-based dynamical system model driven by a Markov input process to present a unified framework for stochastic thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic dissipativity, losslessness and accumulativity theory, we develop a nonlinear stochastic port-Hamiltonian system model characterized by energy conservation and entropy non-conservation laws that are consistent with statistical thermodynamic principles. In particular, we show that the difference between the average stored system energy and the average supplied system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration, whereas the difference between average system entropy production and the average system entropy consumption is a submartingale with respect to the system filtration. This article is part of the theme issue ‘Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)’.

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“…These processes are another difference that NO reveals with conventional neurotransmitters. Consequently, modeling the dynamics of NO implies gathering in the model each and every one of its processes: synthesis or generation, diffusion, and self-regulation, with independence of the type of environment which is producing these dynamics, and for which we will use a nonlinear compartamental dynamical system model [34], [35].…”

Section: A Nitric Oxide Dynamic As Volume Signalmentioning

confidence: 99%

Volume Signaling and Neural-Indexing by Nitric Oxide in Artificial Neural Networks

et al. 2022

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We present a computational study whose objective is to show the capacity of the Nitric Oxide (NO) diffusion for information recovery and indexing related to the classical neural architecture the Sparse Distributed Memory (SDM) has. The study is carried out by introducing NO diffusion dynamics by means of a Multi-compartment based NO Diffusion Model, in the storage process of the SDM. We develop a new SDM model, which we term Sparse Distributed Memory by Nitric Oxide diffusion (SDM-NO). Both of these architectures were computationally analysed. We have showed that the information indexing guided by the Nitric Oxide dynamics has a similar or slightly better behavior to the randomly guided by the SDM. For this study we have used two kinds of patterns, a) binary string patterns with eight bits and b) handwritten characters, that the indexing guided by the Nitric Oxide dynamics shows a similar or a little bit better behaviour to the guided indexing one performed randomly by the SDM. Nevertheless, we have also shown that both of the architectures do not perform well in these memory processes.

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Stochastic Thermodynamics: A Dynamical Systems Approach

Cited by 10 publications

References 51 publications

Maximal power output of a stochastic thermodynamic engine

Maximal power output of a stochastic thermodynamic engine

Stochastic thermodynamics: dissipativity, accumulativity, energy storage and entropy production

Volume Signaling and Neural-Indexing by Nitric Oxide in Artificial Neural Networks

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