article published yes Greg Stephens author Thierry Mora author Gasper Tkacik author 3D494DCA-F248-11E8-B48F-1D18A9856A870000-0002-6699-1455 William Bialek author GaTk department The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding thermodynamics. We find evidence for criticality in a diverging specific heat, which corresponds to large fluctuations in how &quot;surprising&quot; we find individual images, and in the quantitative form of the entropy vs energy. We identify special image configurations as local energy minima and show that average patches within each basin are interpretable as lines and edges in all orientations. https://research-explorer.ista.ac.at/download/2914/5366/IST-2016-401-v1+1_1281.full.pdf application/pdfno American Physical Society2013 eng 0806.2694 00031300610005810.1103/PhysRevLett.110.018701 1101 G. Stephens, T. Mora, G. Tkačik, W. Bialek, Physical Review Letters 110 (2013). Stephens, Greg, et al. “Statistical Thermodynamics of Natural Images.” <i>Physical Review Letters</i>, vol. 110, no. 1, 018701, American Physical Society, 2013, doi:<a href="https://doi.org/10.1103/PhysRevLett.110.018701">10.1103/PhysRevLett.110.018701</a>. G. Stephens, T. Mora, G. Tkačik, and W. Bialek, “Statistical thermodynamics of natural images,” <i>Physical Review Letters</i>, vol. 110, no. 1. American Physical Society, 2013. Stephens G, Mora T, Tkačik G, Bialek W. Statistical thermodynamics of natural images. <i>Physical Review Letters</i>. 2013;110(1). doi:<a href="https://doi.org/10.1103/PhysRevLett.110.018701">10.1103/PhysRevLett.110.018701</a> Stephens G, Mora T, Tkačik G, Bialek W. 2013. Statistical thermodynamics of natural images. Physical Review Letters. 110(1), 018701. Stephens, G., Mora, T., Tkačik, G., &#38; Bialek, W. (2013). Statistical thermodynamics of natural images. <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevLett.110.018701">https://doi.org/10.1103/PhysRevLett.110.018701</a> Stephens, Greg, Thierry Mora, Gašper Tkačik, and William Bialek. “Statistical Thermodynamics of Natural Images.” <i>Physical Review Letters</i>. American Physical Society, 2013. <a href="https://doi.org/10.1103/PhysRevLett.110.018701">https://doi.org/10.1103/PhysRevLett.110.018701</a>. 29142018-12-11T12:00:19Z2025-09-29T13:29:28Z