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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...
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...
Thermodynamic Systems01:06

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of  tea boiling in a kettle. The tea and...
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...

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Related Experiment Video

Updated: Jun 5, 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

Thermodynamic large fluctuations from uniformized dynamics.

David Andrieux1

  • 1Department of Neurobiology and Kavli Institute for Neuroscience, Yale University School of Medicine, New Haven, Connecticut 06510, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces uniformization to calculate thermodynamic large deviation functions for continuous-time Markov processes using discrete-time Markov chains. This method simplifies simulating stochastic trajectories and analyzing fluctuation theorems.

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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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Last Updated: Jun 5, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Stochastic Processes

Background:

  • Large fluctuations provide insights into fine-scale dynamics and non-equilibrium thermodynamics via fluctuation theorems.
  • Current methods for analyzing large deviation properties in continuous-time Markov processes can be computationally intensive.

Purpose of the Study:

  • To develop a computationally efficient method for calculating thermodynamic large deviation functions.
  • To provide a unified framework for analyzing both autonomous and non-autonomous stochastic processes.
  • To enable accurate simulation of stochastic trajectories and their flux statistics.

Main Methods:

  • Utilizing the technique of uniformization to transform continuous-time Markov processes into discrete-time Markov chains.
  • Expressing the time evolution of stochastic processes using a single Poisson rate.
  • Applying the formalism to simulate current fluctuations in a stochastic pump model.

Main Results:

  • Thermodynamic large deviation functions can be derived from discrete-time Markov chains via uniformization.
  • The uniformization procedure offers a simplified and efficient approach for simulating stochastic trajectories.
  • Exact flux statistics are reproduced by the simulated trajectories.

Conclusions:

  • Uniformization provides a powerful theoretical and numerical tool for exploring large deviation properties in stochastic systems.
  • This approach unifies the treatment of continuous-time processes and facilitates efficient simulation.
  • The method is applicable to diverse systems, including the analysis of current fluctuations in stochastic pumps.