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Entropy and the Second Law of Thermodynamics

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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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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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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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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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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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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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  1. Home
  3. Information Geometry Approach To Quantum Stochastic Thermodynamics.
  1. Home
  3. Information Geometry Approach To Quantum Stochastic Thermodynamics.

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Information geometry approach to quantum stochastic thermodynamics.

Laetitia P Bettmann1, John Goold1,2

  • 1Trinity College Dublin, School of Physics, College Green, Dublin 2, D02K8N4, Ireland.

Physical Review. E
|February 20, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

This study links information geometry and stochastic thermodynamics using quantum Fisher information (QFI). The research shows QFI’s incoherent part connects to entropic acceleration and thermodynamic forces, extending classical findings to quantum systems.

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Information Geometry

Background:

  • Recent studies highlight connections between information geometry and stochastic thermodynamics.
  • Fisher Information (FI) with respect to time is a key concept linking these fields.
  • The quantum Fisher metric in Hilbert space is nonunique, necessitating decomposition methods.

Purpose of the Study:

  • To decompose quantum Fisher information (QFI) into metric-independent and metric-dependent parts.
  • To establish links between the incoherent component of QFI, entropic acceleration, and thermodynamic quantities.
  • To generalize classical uncertainty relations and entropy rate bounds to quantum systems and analyze quantum thermodynamic phenomena.

Main Methods:

  • Decomposition of QFI into incoherent and coherent contributions.
  • Analysis of generalized GKS-L (Gorini-Kossakowski-Sudarshan-Lindblad) dynamics.
  • Application of information-geometric analysis to quantum systems and the Mpemba effect.

    • Main Results:

    • The incoherent component of QFI is directly linked to entropic acceleration and thermodynamic forces in GKSL dynamics.
    • A classical uncertainty relation is tightened and shown to hold for quantum systems.
    • A generalized geometric bound on entropy rate for far-from-equilibrium processes is derived, including a quantum contribution.

    Conclusions:

    • The framework successfully captures thermodynamic phenomena, exemplified by its application to the quantum-thermodynamic Mpemba effect.
    • The study provides a unified information-geometric approach to quantum thermodynamics.
    • Established parallels between classical and quantum stochastic thermodynamics are reinforced.