Journal ArticleDOI
Thermodynamics of electrical noise in a class of nonlinear RLC networks
Han-Ngee Tan,J. Wyatt +1 more
TLDR
In this paper, the equilibrium and transient behavior of a class of nonlinear RLC circuits driven externally by deterministic inputs and internally by thermal noise from linear resistors is studied.Abstract:
This paper addresses the equilibrium and transient behavior of a class of nonlinear RLC circuits driven externally by deterministic inputs and internally by thermal noise from linear resistors. Resistor noise is described by the standard Nyquist-Johnson model [1], [2]. Physical principles from thermodynamics are formulated as theorems concerning the stochastic differential equation and the associated forward Kolmogorov equation describing the network and are proved on a rigorous basis. The forward Kolgomorov equation governing the evolution of the probability density for certain capacitor charges and inductor fluxes is shown to be an infinite dimensional dissipative dynamical system in the sense of Willems [3]. By this route we demonstrate that essentially all the principles of thermodynamics for this class of systems can be derived as mathematical consequences of the Nyquist-Johnson model for thermal noise in linear resistors. A significant clarification of thermodynamic theory results from this formulation, since the mathematical framework and a number of specific conclusions are valid for transient as well as equilibrium behavior.read more
Citations
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Journal ArticleDOI
Nonlinear device noise models: Satisfying the thermodynamic requirements
J.L. Wyatt,G.J. Coram +1 more
TL;DR: In this paper, the authors proposed three tests to determine whether a given nonlinear device noise model is in agreement with accepted thermodynamic principles, and applied these tests to several models.
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Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
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Equilibrium description of a particle system in a heat bath
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References
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Stochastic differential equations and diffusion processes
TL;DR: In this article, Stochastic Differential Equations and Diffusion Processes are used to model the diffusion process in stochastic differential equations. But they do not consider the nonlinearity of diffusion processes.
Journal ArticleDOI
Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00
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Fundamentals of Statistical and Thermal Physics
TL;DR: In this article, a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars is presented for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum.
Journal ArticleDOI
Dissipative dynamical systems part I: General theory
TL;DR: In this paper, a general theory of dissipative dynamical systems is presented, where dissipativeness is defined in terms of an inequality involving the storage function and the supply function, which is bounded from below by the available storage and from above by the required supply.
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Deterministic and stochastic optimal control
TL;DR: In this paper, the authors considered the problem of optimal control of Markov diffusion processes in the context of calculus of variations, and proposed a solution to the problem by using the Euler Equation Extremals.