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Related Concept Videos

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 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...
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...
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...
The Entropy as a State Function01:14

The Entropy as a State Function

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...
The Second Law of Thermodynamics01:14

The 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. 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 put...

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Related Experiment Video

Updated: May 7, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Fluctuation theorem for hidden entropy production.

Kyogo Kawaguchi1, Yohei Nakayama

  • 1Department of Physics, The University of Tokyo, Hongo 7-3-1, Tokyo 113-0033, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
PubMed
Summary

Reducing variables in Markovian models can hide entropy production. A new integral fluctuation theorem applies when variables are time-reversal invariant or density functions are symmetric, showing entropy production typically decreases with coarse-graining.

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

Published on: December 4, 2017

Related Experiment Videos

Last Updated: May 7, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

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:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Stochastic Processes

Background:

  • Markovian models are essential for describing dynamic systems.
  • Variable elimination in these models can alter entropy production calculations.
  • Understanding irreversible entropy production is key in non-equilibrium systems.

Purpose of the Study:

  • To investigate the impact of variable elimination on irreversible entropy production in Markovian models.
  • To introduce and analyze the concept of 'hidden entropy production'.
  • To establish conditions under which a fluctuation theorem governs this hidden entropy production.

Main Methods:

  • Analysis of Markovian models with and without specific variables.
  • Derivation of an integral fluctuation theorem for hidden entropy production.
  • Examination of conditions related to time-reversal invariance and density function symmetry.
  • Illustrative example using a stochastic process derived from deterministic dynamics.

Main Results:

  • A novel integral fluctuation theorem for hidden entropy production is presented.
  • The theorem holds when variables are time-reversal invariant or density functions are symmetric.
  • Coarse-graining typically decreases entropy production under these conditions.
  • Cases involving nonequilibrated, time-reversal antisymmetric variables can lead to increased entropy production, violating the theorem.

Conclusions:

  • The study reveals a new fluctuation theorem for hidden entropy production in reduced Markovian dynamics.
  • The findings highlight the importance of variable equilibration and time-reversal properties in thermodynamic reductions.
  • The work provides a framework for understanding how coarse-graining affects entropy production in different dynamic systems.