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LIT-522: Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

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StatusActive — read in full 2026-10-02 (NOTE-413); worth reading as the short paper that turned the entropy-production fluctuation theorem into a finite-time, trajectory-level statement for stochastic, microscopically reversible dynamics, P_F(+ω)/P_R(−ω) = e^{ω}, and derived the Jarzynski equality from it in a line. It also defines the trajectory entropy production ω = ln ρ(x_{−τ}) − ln ρ(x_{+τ}) − βQ that the record's stochastic-thermodynamics papers inherit. Read it knowing that its conditions are stated exactly (finite classical system, constant-intensive-parameter baths, Markovian microscopically reversible dynamics, ω odd under time reversal), and that the steady-state version is formally exact but, by the author's own account, of little practical use.
Tagsthermodynamics, natural-sciences, information-theory
Cited as “paper” byNOTE-413 — Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences
Cited as “source” byTHEORY-431 — For classical systems with Markovian, microscopically reversible dynamics, the entropy production of a trajectory obeys an exact finite-time symmetry against the time-reversed process, P_F(+ω)/P_R(−ω) = e^ω, wherever ω is odd under reversal; Jarzynski's work equality and the mean second law follow as corollaries, and the symmetry constrains fluctuations, not which steady state a system selects

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Gavin E. Crooks (1999), Physical Review E 60(3), 2721–2726 — DOI-10.1103/PhysRevE.60.2721 (preprint arXiv:cond-mat/9901352, 29 January 1999)

Standing in the record

Filed on 2026-10-02 with the critics of Prigogine’s extremum principles, the maximum-entropy-production literature and the fluctuation theorems, at the owner’s request to fill out the record’s coverage of dissipative structures. The anthology does not hold it, and no anthology topic can.

NOTE-413 is the close reading of 2026-10-02, and it placed the work: Active. It is the paper that joined the two exact far-from-equilibrium results of the late 1990s: the entropy-production fluctuation theorem of Evans, Searles, Gallavotti and Cohen, and Jarzynski’s work equality (LIT-517). It derives the second from a generalized form of the first. Seifert’s review (LIT-523) names its work relation the Crooks fluctuation theorem and builds its unification on the same time-reversal argument. The quantum thermodynamics review LIT-010 gives its classical and quantum (Tasaki–Crooks) forms.

For the record’s thermodynamics-of-prediction line, it is the cited background, not the source. Still et al. (LIT-327), whose authors include Crooks, cite this paper as one of the fluctuation theorems that assume a known protocol. Their setup is that of a different paper, Crooks’s 1998 Journal of Statistical Physics article on microscopically reversible Markov systems, which the record does not hold. THEORY-026 rests on an average-level identity and uses no fluctuation theorem. This paper’s ω, though, is the trajectory-level quantity a single-trajectory version of LIT-327’s Eq. 14, the open question NOTE-295 raises, would have to start from.

On Prigogine’s programme it bears only indirectly. Its steady-state theorem, and the Green–Kubo relations it recovers for Gaussian entropy production, are statements about fluctuations in a nonequilibrium steady state that do not assume near-equilibrium. The paper’s opening contrast is exactly that: most relations of nonequilibrium statistical dynamics hold “only in the linear, near-equilibrium regime”, and the fluctuation theorems are the exception. The paper does not discuss extremum principles, Prigogine’s or any other.

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