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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Entropy01:18

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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...
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Entropy02:39

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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...
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Entropy and the Second Law of Thermodynamics01:20

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

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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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The Entropy as a State Function01:14

The Entropy as a State Function

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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...
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Entropy production in a non-Markovian environment.

Aki Kutvonen1, Tapio Ala-Nissila1,2, Jukka Pekola3

  • 1COMP Center of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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This study introduces a non-Markovian model for open systems, revealing new entropy production terms crucial for understanding fluctuation relations in driven systems. These findings extend thermodynamics to small, non-equilibrium scales.

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Area of Science:

  • Physics
  • Non-equilibrium Thermodynamics
  • Statistical Mechanics

Background:

  • Stochastic thermodynamics and fluctuation relations extend classical thermodynamics to small, non-equilibrium systems.
  • Current models often assume Markovian dynamics, which may not hold for driven systems.
  • The validity of the Markovian approximation in non-equilibrium conditions is questionable.

Purpose of the Study:

  • To introduce an explicitly non-Markovian model for open system dynamics.
  • To investigate the impact of system-environment correlations on thermodynamic variables.
  • To derive modified fluctuation relations for entropy in non-equilibrium systems.

Main Methods:

  • Development of a non-Markovian model for open systems.
  • Analysis of correlations between system and environment.
  • Derivation of non-Markovian entropy production terms.
  • Explicit derivation of modified fluctuation relations for an overheated single electron box.

Main Results:

  • Introduced a novel non-Markovian dynamics model for open systems.
  • Identified a new non-Markovian entropy production term arising from system-environment correlations.
  • Demonstrated that non-Markovian components are essential for recovering fluctuation relations.
  • Derived modified fluctuation relations for an overheated single electron box.

Conclusions:

  • The Markovian approximation is insufficient for driven non-equilibrium systems.
  • Non-Markovian dynamics and associated entropy production terms are critical for accurate thermodynamic descriptions.
  • Modified fluctuation relations are necessary to account for non-Markovian effects in small systems.