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Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations

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Abstract

We elaborate and compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for a purely dissipative isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequilibrium steady states and offers the most promising possibility to describe the physically relevant fluctuations around macroscopic averages for time-dependent nonequilibrium systems.

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  1. Department of Materials, Polymer Physics, ETH Zürich, HCI H 543, 8093, Zürich, Switzerland

    Hans Christian Öttinger

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  1. Hans Christian Öttinger
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Öttinger, H.C. Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations. J Stat Phys 138, 1067–1083 (2010). https://doi.org/10.1007/s10955-010-9919-6

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  • DOI: https://doi.org/10.1007/s10955-010-9919-6

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