15,522 research outputs found
Second law, entropy production, and reversibility in thermodynamics of information
We present a pedagogical review of the fundamental concepts in thermodynamics
of information, by focusing on the second law of thermodynamics and the entropy
production. Especially, we discuss the relationship among thermodynamic
reversibility, logical reversibility, and heat emission in the context of the
Landauer principle and clarify that these three concepts are fundamentally
distinct to each other. We also discuss thermodynamics of measurement and
feedback control by Maxwell's demon. We clarify that the demon and the second
law are indeed consistent in the measurement and the feedback processes
individually, by including the mutual information to the entropy production.Comment: 43 pages, 10 figures. As a chapter of: G. Snider et al. (eds.),
"Energy Limits in Computation: A Review of Landauer's Principle, Theory and
Experiments
The power dissipation method and kinematic reducibility of multiple-model robotic systems
This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems
Non-linear estimation is easy
Non-linear state estimation and some related topics, like parametric
estimation, fault diagnosis, and perturbation attenuation, are tackled here via
a new methodology in numerical differentiation. The corresponding basic system
theoretic definitions and properties are presented within the framework of
differential algebra, which permits to handle system variables and their
derivatives of any order. Several academic examples and their computer
simulations, with on-line estimations, are illustrating our viewpoint
Matching in the method of controlled Lagrangians and IDA-passivity based control
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The -method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u
On Necessary and Sufficient Conditions for Differential Flatness
This paper is devoted to the characterization of differentially flat
nonlinear systems in implicit representation, after elimination of the input
variables, in the differential geometric framework of manifolds of jets of
infinite order. We extend the notion of Lie-B\"acklund equivalence, introduced
in Fliess et al. (1999), to this implicit context and focus attention on
Lie-B\"acklund isomorphisms associated to flat systems, called trivializations.
They can be locally characterized in terms of polynomial matrices of the
indeterminate \ddt, whose range is equal to the kernel of the polynomial
matrix associated to the implicit variational system. Such polynomial matrices
are useful to compute the ideal of differential forms generated by the
differentials of all possible trivializations. We introduce the notion of a
strongly closed ideal of differential forms, and prove that flatness is
equivalent to the strong closedness of the latter ideal, which, in turn, is
equivalent to the existence of solutions of the so-called generalized moving
frame structure equations. Two sequential procedures to effectively compute
flat outputs are deduced and various examples and consequences are presented.Comment: Version 3 is the published versio
Mapping Self-Organized Criticality onto Criticality
We present a general conceptual framework for self-organized criticality
(SOC), based on the recognition that it is nothing but the expression,
''unfolded'' in a suitable parameter space, of an underlying {\em unstable}
dynamical critical point. More precisely, SOC is shown to result from the
tuning of the {\em order parameter} to a vanishingly small, but {\em positive}
value, thus ensuring that the corresponding control parameter lies exactly at
its critical value for the underlying transition. This clarifies the role and
nature of the {\em very slow driving rate} common to all systems exhibiting
SOC. This mechanism is shown to apply to models of sandpiles, earthquakes,
depinning, fractal growth and forest-fires, which have been proposed as
examples of SOC.Comment: 17 pages tota
Efficiency of Free Energy Transduction in Autonomous Systems
We consider the thermodynamics of chemical coupling from the viewpoint of
free energy transduction efficiency. In contrast to an external
parameter-driven stochastic energetics setup, the dynamic change of the
equilibrium distribution induced by chemical coupling, adopted, for example, in
biological systems, is inevitably an autonomous process. We found that the
efficiency is bounded by the ratio between the non-symmetric and the
symmetrized Kullback-Leibler distance, which is significantly lower than unity.
Consequences of this low efficiency are demonstrated in the simple two-state
case, which serves as an important minimal model for studying the energetics of
biomolecules.Comment: 4 pages, 4 figure
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