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The Second Law of Thermodynamics01:14

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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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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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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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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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Stochastic dynamics, large deviation principle, and nonequilibrium thermodynamics.

Liu Hong1, Hong Qian2

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This study establishes connections between stochastic dynamics and deterministic equations, revealing the origin of entropy in thermodynamics as an emergent property during the deterministic limit.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Mathematical Physics

Background:

  • Classical irreversible thermodynamics lacks a clear origin for its entropy function.
  • Stochastic processes, like chemical master equations and Fokker-Planck equations, describe dynamics at the mesoscopic level.
  • Understanding the link between microscopic stochasticity and macroscopic deterministic behavior is crucial.

Purpose of the Study:

  • To establish intrinsic connections among mesoscopic stochastic dynamics, deterministic equations, large deviation theory, and macroscopic thermodynamic potentials.
  • To elucidate the origin of the entropy function in classical irreversible thermodynamics.
  • To reveal emergent features in the deterministic limit of Markovian dynamics.

Main Methods:

  • Examining the deterministic limit of a general ε-dependent generator for Markovian dynamics.
  • Analyzing continuous Fokker-Planck equations and discrete chemical master equations as special cases.
  • Utilizing large deviation rate functions to bridge stochastic and deterministic descriptions.

Main Results:

  • Intrinsic connections are established between mesoscopic stochastic dynamics and macroscopic thermodynamic potentials.
  • The origin of the entropy function in classical irreversible thermodynamics is identified.
  • An emergent feature arising from the large deviation rate function during the deterministic limit is revealed for both time-reversible and time-irreversible dynamics.

Conclusions:

  • The entropy function in classical irreversible thermodynamics emerges naturally from the large deviation rate function in the deterministic limit.
  • This framework unifies descriptions of stochastic and deterministic systems, offering insights into fundamental thermodynamic principles.
  • The findings apply to both Hamiltonian (time-reversible) and non-Hamiltonian (time-irreversible) systems.