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Register a new userEnergy Storage in Steady States under Cyclic Local Energy Input
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We study periodic steady states of a lattice system under external cyclic energy supply using simulation. We consider different protocols for cyclic energy supply and examine the energy storage. Under the same energy flux, we found that the stored energy depends on the details of the supply, period and amplitude of the supply. Further, we introduce an adiabatic wall as internal constrain into the lattice and examine the stored energy with respect to different positions of the internal constrain. We found that the stored energy for constrained systems are larger than their unconstrained counterpart. We also observe that the system stores more energy through large and rare energy delivery, comparing to small and frequent delivery.
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Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the system settles in a stationary state, it will be a nonequilibrium steady state (NESS), with time independent probability distribution as well as persistent probability current loops. The observable consequences of the latter are explored. In particular, cyclic behavior of some form must be present: some are prominent and manifest, while others are more obscure and subtle. We present a theoretical framework to analyze such properties, introducing the notion of probability angular momentum and its distribution. Using several examples, we illustrate the manifest and subtle categories and how best to distinguish between them. These techniques can be applied to reveal the NESS nature of a wide range of systems in a large variety of areas. We illustrate with one application: variability of ocean heat content in our climate system.
Systems kept out of equilibrium in stationary states by an external source of energy store an energy $Delta U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $Delta U$ for two model systems: ideal gas and Lennard-Jones fluid. $Delta U$ depends not only on the total energy flux, $J_U$, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where: the energy flux per unit volume is (i) constant; (ii) proportional to the local temperature (iii) proportional to the local density. We show that $Delta U /J_U=tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $tau$ is the characteristic time scale of energy outflow from the system immediately after the shutdown of energy flux. We prove that $tau$ is minimized in stable states of the Rayleigh-Benard cell.
We study a quantity $mathcal{T}$ defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium $U_0$, $Delta U=U-U_0$ divided by the heat flow $J_{U}$ going out of the system. A recent study suggests that $mathcal{T}$ is minimized in steady states (Phys.Rev.E.99, 042118 (2019)). We evaluate this hypothesis using an ideal gas system with three methods of energy delivery: from a uniformly distributed energy source, from an external heat flow through the surface, and from an external matter flow. By introducing internal constraints into the system, we determine $mathcal{T}$ with and without constraints and find that $mathcal{T}$ is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows $U=U_0*f(J_U)$. In this context, we discuss natural variables for NESS, define the embedded energy (an analog of Helmholtz free energy for NESS), and provide its interpretation.
We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasi-static and fnite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.
Systems in which the heat flux depends on the direction of the flow are said to present thermal rectification. This effect has attracted much theoretical and experimental interest in recent years. However, in most theoretical models the effect is found to vanish in the thermodynamic limit, in disagreement with experiment. The purpose of this paper is to show that the rectification may be restored by including an energy-conserving noise which randomly flips the velocity of the particles with a certain rate $lambda$. It is shown that as long as $lambda$ is non-zero, the rectification remains finite in the thermodynamic limit. This is illustrated in a classical harmonic chain subject to a quartic pinning potential (the $Phi^4$ model) and coupled to heat baths by Langevin equations.
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