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Related Concept Videos

Thermodynamic Systems01:06

Thermodynamic Systems

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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...
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Second Law of Thermodynamics02:49

Second Law of Thermodynamics

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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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Second Law of Thermodynamics00:53

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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...
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The Carnot Cycle and the Second Law of Thermodynamics01:20

The Carnot Cycle and the Second Law of Thermodynamics

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The Carnot engine works between two heat reservoirs of fixed temperatures. The Carnot cycle begs the following question: Is it possible to devise a heat engine that is more efficient than a Carnot engine between two fixed temperatures? The answer lies in designing a Carnot refrigerator.
Since the individual steps in a Carnot cycle can be reversed, the entire cycle is, thus, reversible. If a Carnot cycle is reversed, it becomes a Carnot refrigerator. It extracts heat Qc from a cold reservoir at...
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Path Between Thermodynamics States01:21

Path Between Thermodynamics States

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Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
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Conservation of Energy in Control Volume01:14

Conservation of Energy in Control Volume

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Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
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Related Experiment Video

Updated: Jan 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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General linear thermodynamics for periodically driven systems with multiple reservoirs.

Karel Proesmans1, Carlos E Fiore2

  • 1Hasselt University, B-3590 Diepenbeek, Belgium.

Physical Review. E
|October 3, 2019
PubMed
Summary

We developed a linear thermodynamics theory for Markov dynamics, providing formulas for chemical work, heat, and entropy production. This theory applies to steady-state and time-periodic systems, including quantum dots.

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Area of Science:

  • Non-equilibrium statistical mechanics
  • Quantum thermodynamics
  • Theoretical physics

Background:

  • Understanding thermodynamics in non-equilibrium systems is crucial for fields like quantum computing and energy harvesting.
  • Linear response theory provides a framework for analyzing system behavior under small perturbations.
  • Markov dynamics simplifies complex systems by assuming memoryless evolution.

Purpose of the Study:

  • To develop a linear thermodynamics theory for general Markov dynamics under steady-state and time-periodic driving.
  • To derive general expressions for thermodynamic quantities like chemical work, heat, and entropy production.
  • To verify Onsager-Casimir reciprocal relations using derived Onsager coefficients.

Main Methods:

  • Derivation of linear thermodynamics theory for Markov processes.
  • Formulation of thermodynamic quantities using equilibrium probability distribution and driving functions.
  • Calculation of entropy production as a bilinear function of thermodynamic forces and fluxes.
  • Derivation of explicit formulae for Onsager coefficients.

Main Results:

  • General expressions for chemical work, heat, and entropy production derived.
  • Entropy production shown to be a bilinear function of forces and fluxes.
  • Explicit formulae for Onsager coefficients obtained and used to verify Onsager-Casimir reciprocal relations.
  • Theory illustrated with a periodically driven quantum dot model.

Conclusions:

  • The derived linear thermodynamics theory provides a unified framework for analyzing non-equilibrium systems.
  • The results offer insights into the behavior of quantum systems under periodic driving.
  • The study validates fundamental relations in non-equilibrium thermodynamics and discusses optimization protocols.