Reliability and entropy production in nonequilibrium electronic memories

Freitas, Nahuel; Proesmans, Karel; Esposito, Massimiliano

doi:10.1103/physreve.105.034107

Cited by 13 publications

(15 citation statements)

References 30 publications

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“…We assume that a macroscopic limit exists: there is a scaling parameter Ω such that the transition rates scale as Ω and that the typical values of the density x = n/Ω are finite for Ω → ∞. Important examples satisfying the previous assumptions include chemical reaction networks [22][23][24][25][26][27] in the large volume limit, electronic circuits [28,29] in the limit of large capacitances (see example in section VIII-A), and some coarse-grained models of interacting many-body systems [30]. Then, in the limit Ω → ∞, the probability distribution P (x, t) satisfies a large deviations (LD) principle [31,32]:…”

Section: Macroscopic Limit and Large Deviations Principlementioning

confidence: 99%

“…This is in part because of the analogy between Eq. ( 2) and the usual equilibrium Gibbs distribution, but more importantly because f ss (x) can be shown to be a Lyapunov function of the deterministic dynamics [37] (see Appendix B), and provides information about the lifetime of non-equilibrium metastable states, in full analogy to equilibrium reaction-rate theory [29,36,38,39].…”

Section: Macroscopic Limit and Large Deviations Principlementioning

confidence: 99%

“…For the work contributions we will abuse notation and write W ρ (x) = lim Ω→∞ W ρ (n = Ωx). Thus, we consider situations in which the work contributions associated to a transition do not scale with the system size, as is indeed the case in electronic circuits [28,29] and chemical reaction networks [22][23][24][25][26][27]. According to the previous definitions, for large Ω the LDB conditions become:…”

Section: Thermodynamic Structurementioning

confidence: 99%

“…We consider the model of a low-power static random access memory (SRAM) cell developed in [28,29]. The usual CMOS implementation of this kind of memories involves two inverters or NOT gates connected in a loop, each of which is composed of two MOS transistors, as shown in Figure 1-(a).…”

Section: Examples a Cmos Sram Cellmentioning

confidence: 99%

“…Also, all Poisson rates are proportional to I 0 /q e , where I 0 is a characteristic current. Under certain physical scalings of the transistors, as discussed in [29], both I 0 and C increase linearly with the size of the device, and therefore we can take C, or equivalently v −1 e , as the scaling parameter Ω above. Thus, the macroscopic limit Ω → ∞ must in this case be understood as the limit v e /V T → 0 and v e /V dd → 0, where V T = (βq e ) −1 is the thermal voltage.…”

Section: Examples a Cmos Sram Cellmentioning

confidence: 99%

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Linear response in large deviations theory: A method to compute non-equilibrium distributions

Freitas,

Falasco,

Esposito

2021

Preprint

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We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scaleindependent rate function (i.e., a large deviations principle is satisfied). In order to provide an explicit expression for the probability distribution valid away from equilibrium, we propose a linear response theory performed at the level of the rate function. We show that the first order nonequilibrium contribution to the steady state rate function, g(x), satisfies u(x) • ∇g(x) = −β Ẇ (x) where the vector field u(x) defines the macroscopic deterministic dynamics, and the scalar field Ẇ (x) equals the rate at which work is performed on the system in a given state x. This equation provides a practical way to determine g(x), significantly outperforms standard linear response theory applied at the level of the probability distribution, and approximates the rate function surprisingly well in some far-from-equilibrium conditions. The method applies to a wealth of physical and chemical systems, that we exemplify by two analytically tractable models -an electrical circuit and an autocatalytic chemical reaction network -both undergoing a non-equilibrium transition from a monostable phase to a bistable phase. Our approach can be easily generalized to transient probabilities and non-autonomous dynamics. Moreover, its recursive application generates a virtual flow in the probability space which allows to determine the steady state rate function arbitrarily far from equilibrium.

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Section: Macroscopic Limit and Large Deviations Principlementioning

confidence: 99%

Section: Macroscopic Limit and Large Deviations Principlementioning

confidence: 99%

Section: Thermodynamic Structurementioning

confidence: 99%

Section: Examples a Cmos Sram Cellmentioning

confidence: 99%

Section: Examples a Cmos Sram Cellmentioning

confidence: 99%

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Linear response in large deviations theory: A method to compute non-equilibrium distributions

Freitas,

Falasco,

Esposito

2021

Preprint

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On noise-induced transient bit flips in subthreshold SRAM

Brandt

Silveira

Delvenne

et al. 2023

Solid-State Electronics

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Emergent second law for non-equilibrium steady states

Freitas

Esposito

2022

Nat Commun

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The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to non-equilibrium steady states, one must relate the self-information $${{{{{{{\mathcal{I}}}}}}}}(x)=-\!\log ({P}_{{{{{{{{\rm{ss}}}}}}}}}(x))$$ I ( x ) = − log ( P ss ( x ) ) of microstate x to measurable physical quantities. This is a central problem in non-equilibrium statistical physics. By considering open systems described by stochastic dynamics which become deterministic in the macroscopic limit, we show that changes $${{\Delta }}{{{{{{{\mathcal{I}}}}}}}}={{{{{{{\mathcal{I}}}}}}}}({x}_{t})-{{{{{{{\mathcal{I}}}}}}}}({x}_{0})$$ Δ I = I ( x t ) − I ( x 0 ) in steady state self-information along deterministic trajectories can be bounded by the macroscopic entropy production Σ. This bound takes the form of an emergent second law $${{\Sigma }}+{k}_{b}{{\Delta }}{{{{{{{\mathcal{I}}}}}}}}\,\ge \,0$$ Σ + k b Δ I ≥ 0 , which contains the usual second law Σ ≥ 0 as a corollary, and is saturated in the linear regime close to equilibrium. We thus obtain a tighter version of the second law of thermodynamics that provides a link between the deterministic relaxation of a system and the non-equilibrium fluctuations at steady state. In addition to its fundamental value, our result leads to novel methods for computing non-equilibrium distributions, providing a deterministic alternative to Gillespie simulations or spectral methods.

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Reliability and entropy production in nonequilibrium electronic memories

Cited by 13 publications

References 30 publications

Linear response in large deviations theory: A method to compute non-equilibrium distributions

Linear response in large deviations theory: A method to compute non-equilibrium distributions

On noise-induced transient bit flips in subthreshold SRAM

Emergent second law for non-equilibrium steady states

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