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Thermodynamic variational relation.

Domingos S P Salazar1

  • 1Unidade de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil.

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|November 18, 2023
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We introduce a thermodynamic variational relation (TVR) for general observables in systems far from equilibrium. This new framework unifies and extends the thermodynamic uncertainty relation (TUR) for broader applications in statistical physics.

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Area of Science:

  • Statistical physics
  • Non-equilibrium thermodynamics
  • Information theory

Background:

  • The thermodynamic uncertainty relation (TUR) connects observable statistics to entropy production in non-equilibrium systems.
  • Existing TUR derivations often require specific constraints on observables, limiting their general applicability.
  • General observables in fluctuating systems are crucial for understanding complex dynamics.

Purpose of the Study:

  • To develop a generalized thermodynamic relation applicable to any observable in non-equilibrium systems.
  • To establish a variational framework connecting observable statistics and entropy production.
  • To derive a universal thermodynamic uncertainty relation (TUR) and extend it to higher-order statistics.

Main Methods:

  • Utilized the variational representation of f-divergences to establish a connection between general observables and entropy production.
  • Developed a thermodynamic variational relation (TVR) as a unifying theoretical framework.
  • Derived a generalized TUR from the TVR, removing previous parity constraints.

Main Results:

  • Established a novel thermodynamic variational relation (TVR) for arbitrary observables in systems far from equilibrium.
  • Derived a universal thermodynamic uncertainty relation (TUR) applicable beyond asymmetric currents.
  • Obtained new relations for higher-order statistics of observables, enhancing understanding of non-equilibrium fluctuations.

Conclusions:

  • The proposed TVR provides a powerful and general tool for analyzing non-equilibrium systems.
  • This work overcomes limitations of previous TUR formulations, enabling broader applications.
  • The findings offer new insights into the fundamental connections between information, thermodynamics, and fluctuations in complex systems.