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Effective Thermodynamics for a Marginal Observer.

Matteo Polettini1, Massimiliano Esposito1

  • 1Physics and Materials Science Research Unit, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg.

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|December 30, 2017
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Summary
This summary is machine-generated.

Even with incomplete system information, thermodynamics fundamentals like the fluctuation relation (FR) and 2nd law can be maintained. This is achieved by constructing a hidden time reversal for observed marginal currents in statistical thermodynamics.

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Area of Science:

  • Statistical Thermodynamics
  • Non-equilibrium Systems
  • Information Theory

Background:

  • Traditional thermodynamics assumes complete system information, including exact force evaluation and no parasitic currents.
  • The fluctuation relation (FR), a key concept, relies on measurable transitions to characterize processes as Markovian.
  • In practice, observers often measure only marginal currents, leading to incomplete system information.

Purpose of the Study:

  • To demonstrate that an effective thermodynamic description, including the FR and 2nd law, is possible even with incomplete information.
  • To reconcile the measurement of marginal currents with fundamental thermodynamic principles.

Main Methods:

  • Mathematical construction of a hidden time reversal for system dynamics.
  • Incorporating the physical constraint that observed currents represent single transitions in the configuration space.
  • Utilizing a simple abstract example for illustration and exploring generalizations.

Main Results:

  • An effective thermodynamic description can be formulated despite incomplete observer information.
  • The fluctuation relation (FR) and the 2nd law remain valid under these conditions.
  • The approach relies on a hidden time-reversal symmetry and constraints on observed currents.

Conclusions:

  • Fundamental thermodynamic laws are robust and can be applied even when system information is limited.
  • The developed framework provides a method to derive thermodynamic relations from marginal current measurements.
  • This work opens avenues for applying thermodynamics to complex systems with partial observability.