Related Experiment Video
Updated: Apr 29, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
7.6K
Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control
1Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Physical Review Letters
|May 27, 2014
Summary
Feedback control in Langevin processes can become non-Markovian due to time lags. This study modifies dissipation-time reversal relations and extends the second law for nonequilibrium stationary states.
Area of Science:
- Statistical Physics
- Nonlinear Dynamics
- Control Theory
Background:
- Continuous feedback control of Langevin processes can introduce non-Markovian dynamics due to measurement-control time lags.
- Standard relations between dissipation and time reversal may not hold under such conditions.
Purpose of the Study:
- To investigate the consequences of time lags in feedback control on the dynamics of Langevin processes.
- To propose a modified framework for irreversibility and entropy production in nonequilibrium systems with time-delayed control.
- To extend the second law of thermodynamics for these systems.
Main Methods:
- Modification of the fundamental relationship between dissipation and time reversal.
- Inclusion of noncausal contributions in the reverse process analysis.
- Development of a new definition for path irreversibility and trajectory-dependent total entropy production.
- Application to analytically tractable linear systems.
Main Results:
- Time lags in feedback control necessitate adjustments to the dissipation-time reversal relationship.
- A novel quantity for measuring path irreversibility in nonequilibrium stationary states is introduced.
- The proposed definition equates to trajectory-dependent total entropy production.
- An extended second law of thermodynamics is formulated, simplifying in the long-time limit.
Conclusions:
- The study provides a theoretical framework to handle non-Markovian Langevin processes under feedback control with time lags.
- The extended second law offers a more general description of thermodynamic processes in nonequilibrium systems.
- The findings are relevant for systems exhibiting both analytical tractability and experimental applicability.
Related Concept Videos
01:10Entropy Change in Reversible Processes
2.4K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.4K
01:14The Entropy as a State Function
133
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
133
01:26Entropy and the Second Law of Thermodynamics
377
Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
377
01:20Entropy and the Second Law of Thermodynamics
3.3K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
3.3K
01:14The Second Law of Thermodynamics
5.2K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
5.2K
01:24BIBO stability of continuous and discrete -time systems
1.1K
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
1.1K