Methods and conversations in (post)modern thermodynamics

Avanzini, Francesco; Bilancioni, Massimo; Cavina, Vasco; Dal Cengio, Sara; Esposito, Massimiliano; Falasco, Gianmaria; Forastiere, Danilo; Freitas, Jose Nahuel; Garilli, Alberto; Harunari, Pedro E.; Lecomte, Vivien; Lazarescu, Alexandre; Marehalli Srinivas, Shesha G.; Moslonka, Charles; Neri, Izaak; Penocchio, Emanuele; Piñeros, William D.; Polettini, Matteo; Raghu, Adarsh; Raux, Paul; Sekimoto, Ken; Soret, Ariane

doi:10.21468/scipostphyslectnotes.80

SciPost Phys. Lect. Notes

2024

DOI: 10.21468/scipostphyslectnotes.80

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Methods and conversations in (post)modern thermodynamics

Francesco Avanzini,

Massimo Bilancioni,

Vasco Cavina

et al.

Abstract: Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues.

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Cited by 8 publications

References 206 publications

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On the area swept by a biased diffusion till its first-exit time: martingale approach and gambling opportunities

Sarmiento,

Das,

Roldán

2024

Indian J Phys

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On the area swept by a biased diffusion till its first-exit time: martingale approach and gambling opportunities

Sarmiento,

Das,

Roldán

2024

Indian J Phys

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Nonequilibrium thermodynamics of non-ideal reaction–diffusion systems: Implications for active self-organization

Avanzini,

Aslyamov,

Fodor

et al. 2024

The Journal of Chemical Physics

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We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction–diffusion systems, which embodies Flory–Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena, such as liquid–liquid phase separation, coacervation, and the formation of biomolecular condensates.

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Markov generators as non-Hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and singular value decompositions

Monthus

2024

J. Stat. Mech.

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Continuity equations associated with continuous-time Markov processes can be considered as Euclidean Schrödinger equations, where the non-Hermitian quantum Hamiltonian H = div J is naturally factorized into the product of the divergence operator div and the current operator J . For non-equilibrium Markov jump processes in a space of N configurations with M links and C = M − ( N − 1 ) ⩾ 1 independent cycles, this factorization of the N × N Hamiltonian H = I † J involves the incidence matrix I and the current matrix J of size M × N, so that the supersymmetric partner H ^ = J I † governing the dynamics of the currents existing on the M links is of size M × M. To better understand the relations between the spectral decompositions of these two Hamiltonians H = I † J and H ^ = J I † with respect to their bi-orthogonal basis of right and left eigenvectors that characterize the relaxation dynamics towards the steady state and the steady currents, it is useful to analyze the properties of the singular value decomposition of the two rectangular matrices I and J of size M × N and the interpretations in terms of discrete Helmholtz decompositions. This general framework concerning Markov jump processes can be adapted to non-equilibrium diffusion processes governed by Fokker–Planck equations in dimension d, where the number N of configurations, the number M of links and the number C = M − ( N − 1 ) of independent cycles become infinite, while the two matrices I and J become first-order differential operators acting on scalar functions to produce vector fields.

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Methods and conversations in (post)modern thermodynamics

Cited by 8 publications

References 206 publications

On the area swept by a biased diffusion till its first-exit time: martingale approach and gambling opportunities

On the area swept by a biased diffusion till its first-exit time: martingale approach and gambling opportunities

Nonequilibrium thermodynamics of non-ideal reaction–diffusion systems: Implications for active self-organization

Markov generators as non-Hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and singular value decompositions

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