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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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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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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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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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The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other...
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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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Emergent second law for non-equilibrium steady states.

José Nahuel Freitas1, Massimiliano Esposito2

  • 1Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, 162a, avenue de la Faïencerie, Luxembourg, L-1511, Luxembourg, Luxembourg. nahuel.freitas@uni.lu.

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This study extends the Gibbs distribution to non-equilibrium systems by linking self-information changes to entropy production. An emergent second law is derived, offering new methods for computing non-equilibrium distributions.

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Area of Science:

  • Non-equilibrium statistical physics
  • Thermodynamics
  • Stochastic processes

Background:

  • The Gibbs distribution is fundamental for thermal equilibrium states.
  • Extending this to non-equilibrium steady states requires linking self-information to measurable quantities.
  • This is a central challenge in statistical physics.

Purpose of the Study:

  • To develop a theoretical framework for non-equilibrium steady states.
  • To establish a connection between self-information dynamics and macroscopic entropy production.
  • To derive a generalized second law of thermodynamics.

Main Methods:

  • Analysis of open systems with stochastic dynamics.
  • Considering the macroscopic limit where dynamics become deterministic.
  • Bounding changes in steady-state self-information along deterministic trajectories.

Main Results:

  • An emergent second law, [Formula: see text], bounding self-information changes by entropy production (Σ).
  • The derived law includes the standard second law (Σ ≥ 0) as a corollary.
  • The bound is saturated in the linear regime near equilibrium.

Conclusions:

  • A tighter version of the second law of thermodynamics is established.
  • This provides a link between deterministic system relaxation and non-equilibrium fluctuations.
  • Novel deterministic methods for computing non-equilibrium distributions are proposed.