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Related Concept Videos

Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
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...
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...
Second Law of Thermodynamics00:53

Second Law of Thermodynamics

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the chemical energy...
Internal Energy and Formulation of the First Law01:19

Internal Energy and Formulation of the First Law

In thermodynamics, energy is used to describe and predict the behavior of physical systems. The internal energy (U) of a system is the sum of all microscopic forms of energy within the system, including molecular kinetic and potential energies, as well as contributions from electronic and nuclear energy levels. Although the individual components of internal energy cannot be measured directly, the internal energy of any system is well defined within thermodynamic theory.The first law of...
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...

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Related Experiment Video

Updated: Jun 20, 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

Variational formulation of stochastic thermodynamics: Finite-dimensional systems.

Héctor Vaquero Del Pino1, François Gay-Balmaz2, Hiroaki Yoshimura3

  • 1Nanyang Technological University, Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, 21 Nanyang Link, Singapore 637371.

Physical Review. E
|June 19, 2026
PubMed
Summary

This study establishes a variational foundation for stochastic thermodynamics, ensuring the second law and revealing new fluctuation-dissipation relations for various systems. It offers a unified geometric framework for thermodynamic modeling.

Related Experiment Videos

Last Updated: Jun 20, 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
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Stochastic thermodynamics describes systems with inherent randomness.
  • Existing models face challenges with complex systems and cross-correlated noise.
  • A unified framework is needed for broader applications.

Purpose of the Study:

  • Develop a variational foundation for stochastic thermodynamics.
  • Incorporate the second law to derive a consistent thermodynamic structure.
  • Extend key results to diverse systems, including open and closed ones.

Main Methods:

  • Utilizing a generalized Lagrange-d'Alembert principle within a geometric framework.
  • Implementing nonlinear nonholonomic constraints for irreversible and stochastic forces.
  • Treating entropy as an independent dynamical variable.

Main Results:

  • Emergence of novel generalized fluctuation-dissipation relations.
  • Ensured local detailed balance and consistency with the second law.
  • Unified description applicable to individual trajectories and extended phase space.

Conclusions:

  • The variational approach provides a thermodynamically consistent modeling method.
  • The framework accommodates complex features like state-dependent parameters and cross-correlated noise.
  • Potential applications in continuum systems like active and complex fluids.