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Entropy, irreversibility and inference at the foundations of statistical physics

Nature Reviews Physics (2024)Cite this article

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Abstract

Statistical physics relates the properties of macroscale systems to the distributions of their microscale agents. Its central tool has been the maximization of entropy, an equilibrium variational principle. Recent work has sought extensions to non-equilibria: across processes of change both fast and slow, in the Jarzynski equality and fluctuation relations and other tools of stochastic thermodynamics, using large deviation theory or others. When recognized as an inference principle, entropy maximization can be generalized for non-equilibria and applied to path entropies rather than state entropies, becoming the principle of maximum caliber, which we emphasize in this Review. Our primary goal is to enhance crosstalk among researchers working in disparate silos, comparing and contrasting different approaches while pointing to common roots.

Key points

  • The original concept of equilibrium thermodynamic entropy has branched into two related but distinct concepts, both termed entropy: one a tool for inference and the other a measure of time irreversibility.

  • The field of stochastic thermodynamics and the methods therein have developed the irreversibility version of entropy, extracting many important results, although some of those results are limited in interpretation to near equilibrium.

  • Although many problems in statistical physics can be formulated in terms of multiple approaches, the Bayesian inferential approach provides the most general and solid footing.

  • In analogy with the maximum entropy inference approach to equilibrium thermodynamic states, the maximum caliber principle performs inference with path entropies, serving as a powerful generative procedure for making models in statistical physics and beyond.

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Fig. 1: The generative inference pipeline of equilibrium statistical physics, which generates the microscopic probability distribution from the input assertions.
Fig. 2: Hamiltonian-constrained non-equilibrium modelling.
Fig. 3: Bath-constrained non-equilibrium modelling.
Fig. 4: Local detailed balance.
Fig. 5: The generative inference pipeline of non-equilibrium statistical physics, which generates the pathway distribution from the input assertions.

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Acknowledgements

The authors are grateful to the Stony Brook University Laufer Center for support. The authors also thank B. Cannon, C. Jarzynski, C. Kocher, S. Pressé, D. Sivak and J. Wang for insightful comments and helpful feedback.

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  1. Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY, USA

    Jonathan Asher Pachter, Ying-Jen Yang & Ken A. Dill

  2. Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA

    Jonathan Asher Pachter & Ken A. Dill

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Pachter, J.A., Yang, YJ. & Dill, K.A. Entropy, irreversibility and inference at the foundations of statistical physics. Nat Rev Phys (2024). https://doi.org/10.1038/s42254-024-00720-5

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