Housekeeping Entropy Production

Nonequilibrium steady states decompose total entropy production into housekeeping (maintained by nonconservative forces) and excess (transient) parts. Explore the Hatano-Sasa relation and current-force structure.

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σ_total (k_B/s)

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σ_hk (housekeeping)

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σ_ex (excess)

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Hatano-Sasa ⟨e^-Y⟩

Controls

Thermodynamic Force F2.0

Steady-State Current J1.0

Driving (nonconservative)1.0

Temperature T1.0

Theory

σ_total = J · F ≥ 0
σ_hk = J · F_nc (housekeeping)
σ_ex = J · F_c (excess/transient)

Hatano-Sasa (2001):
⟨exp(−Y)⟩_ss = 1
Y = ∫ (∂_t φ) dt / T

Second law:
σ_hk ≥ 0, σ_ex ≥ 0