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The Second Law of Thermodynamics01:14

The 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. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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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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Third Law of Thermodynamics02:38

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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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.
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...
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Second Law of Thermodynamics02:49

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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...
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Entropy Change in Reversible Processes01:10

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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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Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
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Universal Relation between Entropy and Kinetics.

Benjamin Sorkin1, Haim Diamant1, Gil Ariel2

  • 1School of Chemistry and Center for Physics and Chemistry of Living Systems, Tel Aviv University, 69978 Tel Aviv, Israel.

Physical Review Letters
|October 20, 2023
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Summary
This summary is machine-generated.

This study derives a universal inequality linking entropy and particle dynamics, applicable even far from equilibrium. This provides new ways to bound or estimate diffusion coefficients using entropy, or vice versa.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • Relating thermodynamic and kinetic properties is a long-standing challenge.
  • Understanding systems far from thermodynamic equilibrium is crucial.

Purpose of the Study:

  • Derive a rigorous, universal inequality between entropy and dynamic properties.
  • Establish a connection between entropy and diffusion coefficients in steady states.

Main Methods:

  • First-principles derivation of a general inequality.
  • Application to diffusive dynamics, including normal and anomalous diffusion.
  • Analysis of steady states arbitrarily far from thermodynamic equilibrium.

Main Results:

  • A universal inequality relating entropy and the dynamic propagator of particle configurations.
  • A specific relation between entropy and the diffusion coefficient for diffusive systems.
  • Demonstrated utility in bounding diffusion coefficients from entropy and vice versa.

Conclusions:

  • The derived relation offers a powerful tool for analyzing systems far from equilibrium.
  • Provides a method to estimate thermodynamic properties from kinetic data and vice versa.
  • Highlights broad applicability in diverse physical systems.