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Related Concept Videos

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...
The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
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...
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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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Entropy fluctuation theorems in driven open systems: application to electron counting statistics.

Massimiliano Esposito1, Upendra Harbola, Shaul Mukamel

  • 1Department of Chemistry, University of California, Irvine, California 92697, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
Summary
This summary is machine-generated.

This study introduces three fluctuation theorems (FTs) for entropy production in driven systems, revealing a universal inequality for nonequilibrium transformations. These findings offer new insights into thermodynamics and experimental verification methods.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Systems

Background:

  • Externally driven systems exchanging energy and matter with reservoirs are fundamental in nonequilibrium thermodynamics.
  • Master equations describe the dynamics of such systems, but quantifying entropy production under driving is complex.
  • Fluctuation theorems (FTs) provide powerful tools for understanding entropy production in nonequilibrium processes.

Purpose of the Study:

  • To express total entropy production as a sum of contributions from nonequilibrium initial conditions, external driving, and broken detailed balance.
  • To derive three integral fluctuation theorems (FTs) for these contributions.
  • To establish a universal inequality for arbitrary nonequilibrium transformations and demonstrate experimental testability.

Main Methods:

  • Derivation of three integral fluctuation theorems (FTs) for distinct entropy production mechanisms.
  • Formulation of a universal inequality relating nonequilibrium transformations to adiabatic processes.
  • Simulation of entropy probability distributions for electron transport in a quantum dot.

Main Results:

  • Total entropy production is decomposed into three contributions: initial conditions, external driving, and broken detailed balance.
  • A universal inequality is derived: nonequilibrium transformations yield greater or equal entropy change compared to adiabatic transformations.
  • Previously known FTs are recovered as special cases of the derived theorems.
  • Experimental testability is demonstrated via simulations of electron counting statistics in a quantum dot.

Conclusions:

  • The derived FTs and universal inequality provide a comprehensive framework for analyzing entropy production in driven systems.
  • The study highlights the fundamental relationship between the rate of transformation and entropy production.
  • The proposed experimental setup offers a viable pathway for validating these theoretical predictions in mesoscopic systems.