# Talk: network methods for nonequilibrium thermodynamics

Here my personal notes for the mixed blackboard/slide talk I gave last Monday in Aachen.

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About myself: I work in the group of Massimiliano Esposito, “late Brussels school” (after Prigogine), section of Luxembourg. Culturally more connected to Van Kampen, Onsager etc. But I like Prigogine’s system-theoretic approach, broad overview & culture. I work on the foundations of NonEquilibrium Statistical Mechanics, Chemical Networks dynamics and thermodynamics, algebraic graph theory. But also have projects on: thermodynamics constraints on metabolic modeling of cells, thermodynamics of computation, thermodynamics of quantum open systems. All those things where thermodynamics does not apply, according to some of the speakers…

1. A system-theoretic view on thermodynamics

[open systems; are there isolated systems?; microscopic derivations: Boltzmann’s molecular chaos, the Lindblad equation for OQS, the measurement process, etc. flows of currents (dynamics) powered by forces (thermo); of what? information as the ultimate unit; type of autonomous nonequilibrium: NESS vs. transient; optional: my problem with state functions, why the second law as increase of entropy does not make sense, science as a theory of observations, not of “Nature”; let’s leave the ultimate questions to the priests]

2. Why Markov processes

[Historical reasons: Boltzmann, Einstein, Onsager, Prigogine etc. Essential reasons: temperature is noise! If not, it would be energy, and we could resolve small differentials and use them in smart ways… On Markov: We are assuming a property, not an equation! Currents as stochastic variables, w.r.t. some p.d.f.]

3. Why networks, and in what sense: Algebraic graph theory

[internal vs. external currents; Kirchhoff’s current law (currents) and loop law (forces); types of nonequilibrum in terms of KLL and KCL; topological vs. algebraic network structures; introducing the single-edge assumption]

4. Well-known results from Non-Equilibrium Statistical Mechanics: the fluctuation relations, response theory

[assumption of “completeness”; inference diagram: FR -> IFR -> S-FDR, FR -> RR, IFR -> 2nd Law, detailed balance iff equilibrium]

5. Further results

[the paradigm of “activity,” better bounds on efficiency, etc.]

6. Interlude: The problem with experimental tests, what kind of science is thermodynamics?

7. The marginal problem: outline

[keywords: marginal, hidden, effective, operational; optional: why science is always so]

8. Well-known results go marginal

[what remains of the inference diagram; a clear-cut experimental prediction; the core requirement on parametrization; restoring the rest of the diagram with marginal TR; what happens with phenomenological currents]

9. The main mathematical results behind the construction: Large Deviations

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BIBLIOGRAPHY

[schnakenberg76] J. Schnakenberg, “Network theory of microscopic and macroscopic behavior of master equation systems”, 1976 Rev. Mod. Phys. 48, 571.

[maes18] C. Maes, Non-dissipative effects in nonequilibrium systems, https://fys.kuleuven.be/itf/staff/christ/files/pdf/pub/nondissi12june2017.pdf, to appear in SpringerBriefs (2018).

[polettini18] M. Polettini, M. Esposito, “Marginal fluctuation and response theory”, to appear soon on arXiv.

[polettini17] M. Polettini and M. Esposito, “Effective thermodynamics for a marginal observer”, Phys. Rev. Lett. 119, 240601 (2017).

[altaner16] B. Altaner, M. Polettini, and M. Esposito, Fluctuation-Dissipation Relations Far from Equilibrium, Phys. Rev. Lett. 117, 180601 (2016).

[polettini16] M. Polettini, G. Bulnes Cuetara, M. Esposito, “Conservation laws and symmetries in stochastic thermodynamics”, Phys. Rev. E 94, 052117 (2016).