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Related Concept Videos

Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

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...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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.
Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

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Related Experiment Video

Updated: May 30, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Stochastic thermodynamics for delayed Langevin systems.

Huijun Jiang1, Tiejun Xiao, Zhonghuai Hou

  • 1Hefei National Laboratory for Physical Science at Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary

Stochastic thermodynamics for delayed Langevin systems redefines the second law. A new dissipation functional R obeys R≥0, validating a modified second law and fluctuation theorem even with negative total entropy changes.

Related Experiment Videos

Last Updated: May 30, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Physics
  • Statistical Mechanics
  • Non-equilibrium Thermodynamics

Background:

  • Stochastic thermodynamics (ST) traditionally analyzes systems without time delays.
  • Conventional second law of thermodynamics (Δs(tot))≥0 may not hold for systems with time delays.
  • Time delays introduce additional entropy flux, complicating thermodynamic analysis.

Purpose of the Study:

  • To extend stochastic thermodynamics principles to delayed Langevin systems.
  • To redefine the second law and energy balance for systems with time delays.
  • To introduce and validate a new dissipation functional for delayed systems.

Main Methods:

  • General principles of stochastic thermodynamics.
  • Fokker-Planck description to introduce a delay-averaged dissipation functional η[χ(t)].
  • Inversing-mapping approach to derive delay-averaged force F(x,t) from stationary distribution.

Main Results:

  • A first-law-like energy balance and trajectory-dependent entropy s(t) are defined for delayed systems.
  • The conventional second law is modified; a new functional R=Δs+η obeys (R)≥0.
  • The integral fluctuation theorem (e(-R))=1 holds for the delayed system.
  • Numerical results confirm negative total entropy changes are possible with positive delay feedback.

Conclusions:

  • The study successfully extends stochastic thermodynamics to delayed Langevin systems.
  • A modified second law and fluctuation theorem are established for these systems.
  • The findings provide a theoretical framework for understanding thermodynamics in systems with time delays.