Thermodynamic and stochastic theory of electrical circuits

Journal Article · Sat Feb 15 04:00:00 EST 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.2201· OSTI ID:7280582

Hjelmfelt, A; Ross, J ^[1]

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1. Department of Chemistry, Stanford University, Stanford, California 94305 (United States)

We begin the development of a thermodynamic and stochastic theory of electrical circuits approaching nonequilibrium stationary states containing linear or nonlinear capacitors, resistors, and inductors. We restrict ourselves to circuits with only point attractors. The theory centers around a function {phi}, and we show that: (1) it is the macroscopic driving force to a stationary state, (2) it is a global Liapunov function, (3) it provides necessary and sufficient conditions for the existence and stability of stationary states, (4) its time derivative is a component of the total dissipation, (5) it is an excess work of moving the circuit away from the stationary state, and (6) it determines a stationary probability distribution of a Fokker-Planck equation. The generalization from linear to nonlinear circuits is made with the concept of an instantaneous mapping from the nonlinear circuit to a thermodynamically and kinetically equivalent linear circuit. A translation of chemical to electrical networks holds at the thermodynamic but not stochastic level of description.

• OSTI ID: 7280582
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 45:4; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
426000* -- Engineering-- Components
Electron Devices & Circuits-- (1990-)
CAPACITORS
CHEMICAL REACTIONS
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
ELECTRICAL EQUIPMENT
ELECTRONIC CIRCUITS
ENERGY LOSSES
EQUATIONS
EQUILIBRIUM
EQUIPMENT
EVALUATION
FLUCTUATIONS
FOKKER-PLANCK EQUATION
INDUCTION
LOSSES
LYAPUNOV METHOD
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
RESISTORS
STABILITY
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES
THERMODYNAMICS
VARIATIONS