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Related Concept Videos

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.
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Maxwell's Thermodynamic Relations01:23

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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.
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Third Law of Thermodynamics02:38

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The Zeroth Law of Thermodynamics01:14

The Zeroth Law of Thermodynamics

Systems in mechanical equilibrium exert equal pressure on the separating wall. Similarly, systems in thermal equilibrium share a common thermodynamic property: temperature.Temperature is a measure of the average kinetic energy of particles within a system. More generally, it reflects the internal energy state of the system. The higher the temperature, the more energy a system has, given that other variables, such as volume and pressure, remain constant. However, temperature is not a form of...
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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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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...

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Updated: May 13, 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 length for far-from-equilibrium quantum systems.

Sebastian Deffner1, Eric Lutz

  • 1Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 19, 2013
PubMed
Summary
This summary is machine-generated.

We derived a new lower bound for entropy production in quantum systems, using the Bures angle to measure deviation from equilibrium. This thermodynamic length is valid even far from equilibrium.

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Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Quantum information theory

Background:

  • Understanding entropy production is crucial for characterizing irreversible processes in quantum systems.
  • Existing bounds on entropy production often rely on approximations or are limited to near-equilibrium conditions.
  • The Bures angle offers a geometric measure for distinguishing between quantum states.

Purpose of the Study:

  • To derive a general lower bound on entropy production for a closed quantum system driven by external parameters.
  • To express this bound in terms of the Bures angle between non-equilibrium and equilibrium states.
  • To demonstrate the applicability of this bound using a specific physical model.

Main Methods:

  • Consideration of a closed quantum system initially in thermal equilibrium.
  • Derivation of a lower bound on entropy production.
  • Expression of the bound using the Bures angle between quantum states.
  • Application to a time-dependent harmonic oscillator model.

Main Results:

  • A novel lower bound on entropy production is derived.
  • The bound is expressed as a function of the Bures angle, representing a thermodynamic length.
  • This thermodynamic length is valid arbitrarily far from equilibrium.
  • Analytic expressions for entropy production are obtained for a driven harmonic oscillator.

Conclusions:

  • The Bures angle provides a powerful tool for quantifying entropy production in driven quantum systems.
  • The derived thermodynamic length offers a universal measure of irreversibility, applicable beyond near-equilibrium regimes.
  • The results pave the way for deeper understanding of non-equilibrium quantum thermodynamics.