scholarly journals Proof of the finite-time thermodynamic uncertainty relation for steady-state currents

2017 ◽  
Vol 96 (2) ◽  
Author(s):  
Jordan M. Horowitz ◽  
Todd R. Gingrich
Keyword(s):  
Steady State ◽  
Finite Time ◽  
Uncertainty Relation

scholarly journals Quantumness and thermodynamic uncertainty relation of the finite-time Otto cycle

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Sangyun Lee ◽  
Meesoon Ha ◽  
Hawoong Jeong
Keyword(s):  
Finite Time ◽  
Uncertainty Relation ◽  
Otto Cycle

scholarly journals Fluctuation–response inequality out of equilibrium

2020 ◽  
Vol 117 (12) ◽  
pp. 6430-6436 ◽  
Author(s):  
Andreas Dechant ◽  
Shin-ichi Sasa
Keyword(s):  
Steady State ◽  
Uncertainty Relation ◽  
Stochastic Dynamics ◽  
Direct Consequence ◽  
Transport Processes ◽  
Unperturbed System ◽  
Mean Velocity ◽  
Leibler Divergence ◽  
Probability Densities ◽  
Local Mean

We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation–response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback–Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a “virtual” perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.

A finite-time adaptive robust control for a spacecraft attitude control considering actuator fault and saturation with reduced steady-state error

2018 ◽  
Vol 41 (4) ◽  
pp. 1002-1009 ◽  
Author(s):  
Seyed Majid Smaeilzadeh ◽  
Mehdi Golestani
Keyword(s):  
Steady State ◽  
Upper Bound ◽  
Finite Time ◽  
Attitude Control ◽  
Fault Tolerant ◽  
Adaptive Robust Control ◽  
Significant Feature ◽  
Actuator Fault ◽  
Finite Time Convergence ◽  
State Error

This paper addresses the problem of attitude control of a spacecraft in the presence of model uncertainty, external disturbance, actuator fault and saturation. By introducing a novel form of integral backstepping control, a finite-time fault tolerant control is designed to obtain satisfactory performance, rapid convergence of the system states, reduced steady-state error and high robustness. Guaranteeing finite-time convergence of the attitude trajectory is a significant feature of the proposed control law that is critical in fault tolerant systems. Since the upper bound of the system uncertainty and disturbance is quite difficult to obtain, an adaptation mechanism is presented under which there is no need to know this upper bound. Not only finite-time convergence of the attitude trajectory is proved using the Lyapunov analysis, but also the actuator saturation and fault are taken into account while designing the controller. Simulation results verify the effectiveness and performance of the presented approach.

scholarly journals Transition to blow-up in a reaction–diffusion model with localized spike solutions

2017 ◽  
Vol 28 (6) ◽  
pp. 1015-1055 ◽  
Author(s):  
V. ROTTSCHÄFER ◽  
J. C. TZOU ◽  
M.J. WARD
Keyword(s):  
Steady State ◽  
Linear Stability ◽  
Finite Time ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Linear Stability Theory ◽  
Saddle Node ◽  
Reaction Diffusion Model ◽  
Non Local ◽  
Blow Up Rate

For certain singularly perturbed two-component reaction–diffusion systems, the bifurcation diagram of steady-state spike solutions is characterized by a saddle-node behaviour in terms of some parameter in the system. For some such systems, such as the Gray–Scott model, a spike self-replication behaviour is observed as the parameter varies across the saddle-node point. We demonstrate and analyse a qualitatively new type of transition as a parameter is slowly decreased below the saddle node value, which is characterized by a finite-time blow-up of the spike solution. More specifically, we use a blend of asymptotic analysis, linear stability theory, and full numerical computations to analyse a wide variety of dynamical instabilities, and ultimately finite-time blow-up behaviour, for localized spike solutions that occur as a parameter β is slowly ramped in time below various linear stability and existence thresholds associated with steady-state spike solutions. The transition or route to an ultimate finite-time blow-up can include spike nucleation, spike annihilation, or spike amplitude oscillation, depending on the specific parameter regime. Our detailed analysis of the existence and linear stability of multi-spike patterns, through the analysis of an explicitly solvable non-local eigenvalue problem, provides a theoretical guide for predicting which transition will be realized. Finally, we analyse the blow-up profile for a shadow limit of the reaction–diffusion system. For the resulting non-local scalar parabolic problem, we derive an explicit expression for the blow-up rate near the parameter range where blow-up is predicted. This blow-up rate is confirmed with full numerical simulations of the full PDE. Moreover, we analyse the linear stability of this solution that blows up in finite time.

scholarly journals Sliding Mode Cooperative Control for Multirobot Systems: A Finite-Time Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Masood Ghasemi ◽  
Sergey G. Nersesov
Keyword(s):  
Steady State ◽  
Multiagent Systems ◽  
Finite Time ◽  
Cooperative Control ◽  
Sliding Mode ◽  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Time Stability ◽  
Control Approach ◽  
Finite Time Stability

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. We consider a group of agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. We further extend these results to multiagent systems involving underactuated dynamical agents such as mobile wheeled robots. For this case, we show that while the position variables can be coordinated in finite time, the orientation variables converge to the steady states asymptotically. Finally, we validate our results experimentally using a wheeled mobile robot platform.

Conditions Under Which a Markov Chain Converges to its Steady State in Finite Time

1988 ◽  
Vol 2 (3) ◽  
pp. 377-382 ◽  
Author(s):  
Peter W. Glynn ◽  
Donald L. Iglehart
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Steady State ◽  
Discrete Time ◽  
Continuous Time ◽  
Finite Time ◽  
Transition Matrix ◽  
Continuous Time Markov Chain ◽  
Transient Problem ◽  
Steady State Simulation

Analysis of the initial transient problem of Monte Carlo steady-state simulation motivates the following question for Markov chains: when does there exist a deterministic Tsuch that P{X(T) = y|(0) = x} = ®(y), where ρ is the stationary distribution of X? We show that this can essentially never happen for a continuous-time Markov chain; in discrete time, such processes are i.i.d. provided the transition matrix is diagonalizable.

Finite-Time Thermodynamic Performance for a Class of Irreversible Heat Pumps

1997 ◽  
Author(s):  
Chih Wu ◽  
Lingen Chen ◽  
Fengrui Sun
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Heat Pump ◽  
Finite Time ◽  
Heat Pumps ◽  
Coefficient Of Performance ◽  
Cooling Load ◽  
Heat Leak ◽  
Thermodynamic Performance ◽  
The Relationship

The effect of heat resistance and heat leak on the performance of irreversible heat pumps using a generalized heat transfer law is analyzed in this paper. The relationship between the optimal cooling load and the cop (coefficient of performance) for a steady-state irreversible heat pump is derived.

scholarly journals Exact results for the finite time thermodynamic uncertainty relation

2018 ◽  
Vol 51 (11) ◽  
pp. 11LT01 ◽  
Author(s):  
Sreekanth K Manikandan ◽  
Supriya Krishnamurthy
Keyword(s):  
Finite Time ◽  
Uncertainty Relation ◽  
Exact Results
Sign in / Sign up

Export Citation Format

Share Document