[1] R Clausius, ̈Uber eine ver ̈anderte Form des zweiten Hauptsatzes der mechanischen W ̈armetheorie, Annalen der Physik. xciii(12), 481, (1854).
https://doi.org/10.1002/andp.18541691202
[2] C E Shannon, A mathematical theory of communication, The Bell system technical journal 27(3), 379, (1948).
https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
[3] S Martiniani, P M Chaikin, D Levine, Quantifying hidden order out of equilibrium, Phys. Rev. X 9, 011031, (2019).
https://doi.org/10.1103/PhysRevX.9.011031
[4] S Martiniani, Y Lemberg, P M Chaikin, et al., Correlation lengths in the language of computable information, Phys. Rev. Lett. 125, 170601, (2020).
https://doi.org/10.1103/PhysRevLett.125.170601
[5] R Avinery, M Kornreich, R Beck, Universal and Accessible Entropy Estimation Using a Compression Algorithm, Phys. Rev. Lett. 123, 178102, (2019).
https://doi.org/10.1103/PhysRevLett.123.178102
[6] A Cavagna, P M Chaikin, D Levine, et al., Vicsek model by time-interlaced compression: A dynamical computable information density, Phys. Rev. E 103, 062141, (2021).
https://doi.org/10.1103/PhysRevE.103.062141
[7] S Ro, B Guo, A Shih, T V Phan, et al., Model-Free Measurement of Local Entropy Production and Extractable Work in Active Matter, Phys. Rev. Lett. 129, 220601, (2022).
https://doi.org/10.1103/PhysRevLett.129.220601
[8] D A Wiley, S H Strogatz, M Girvan, The size of a sync basin, Chaos 16(1), 015103, (2006).
https://doi.org/10.1063/1.2165594
[9] S P Cornelius, W L Kath, A E Motter, Realistic control of network dynamics, Nat. Commun. 4(1), 1, (2013).
https://doi.org/10.1038/ncomms2939
[10] Y Zhang, S H Strogatz, Basins with tentacles, Phys. Rev. Lett. 127, 194101, (2021).
https://doi.org/10.1103/PhysRevLett.127.194101
[11] D Frenkel, A J Ladd, New Monte Carlo mehod to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres, J. Chem. Phys. 81(7), 3188, (1984).
https://doi.org/10.1063/1.448024
[12] N Xu, D Frenkel, A J Liu, Direct determination of the size of basins of attraction of jammed solids, Phys. Rev. Lett. 106(24), 245502, (2011).
https://doi.org/10.1103/PhysRevLett.106.245502
[13] D Asenjo, F Paillusson, D Frenkel, Numerical calculation of granular entropy, Phys. Rev. Lett. 112(9), 098002, (20114).
https://doi.org/10.1103/PhysRevLett.112.098002
[14] S Martiniani, K J Schrenk, K Pamola, et al., Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming, Nat. Phys. 13, 848, (2017).
https://doi.org/10.1038/nphys4168
[15] S Martiniani, K J Schrenk, J D Stevenson, et al., Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings, Phys. Rev. E 93(1), 012906, (2016).
https://doi.org/10.1103/PhysRevE.93.012906
[16] S Martiniani, K J Schrenk, J D Stevenson, et al., Structural analysis of high-dimensional basins of attraction, Phys. Rev. E 93(3), 031301, (2016).
https://doi.org/10.1103/PhysRevE.94.031301
[17] D Frenkel, K J Schrenk, S Martiniani, Monte Carlo sampling for stochastic weight functions, Proc. Nat. Ac. Sci. 114(27), 6924, (2017).
https://doi.org/10.1073/pnas.1620497114
[18] S S Ashwin, J Blawzdziewicz, C S O'Hern, et al., Calculations of the structure of basin volumes for mechanically stable packings, Phys. Rev. E 85, 061307, (2012).
https://doi.org/10.1103/PhysRevE.85.061307
[19] M R Shirts, J D Chodera, Statistically optimal analysis of samples from multiple equilibrium states, J. Chem. Phys. 129(12), 124105, (2008).
https://doi.org/10.1063/1.2978177
[20] X Ding, J Vilseck, C Brooks, Fast Solver for Large Scale Multistate Bennett Acceptance Ratio Equations, J. Chem. Theory Comput. 2019(15), 802, (2019).
https://doi.org/10.1021/acs.jctc.8b01010
[21] J G Kirkwood, Statistical Mechanics of Fluid Mixtures, J. Chem. Phys. 3, 300, (1935).
https://doi.org/10.1063/1.1749657
[22] A Gelman, X-L Meng, Simulating normalizing constants: from importance sampling to bridge sampling to path sampling, Statist. Sci. 13(2), 185, (1998).
https://doi.org/10.1214/ss/1028905934
[23] A Bunker, B D ̈unweg, Parallel excluded volume tempering for polymer melts, Phys. Rev. E 63(1), 016701, (2000).
https://doi.org/10.1103/PhysRevE.63.016701
[24] H Fukunishi, O Watanabe, S Takada, On the hamiltonian replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction, J. Chem. Phys. 116(20), 9058, (2002).
https://doi.org/10.1063/1.1472510
[25] J M Torrie, J P Valleau, Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling, J. Comput. Phys. 23(2), 199, (1977).
https://doi.org/10.1016/0021-9991(77)90121-8
[26] A Chevallier, F Cazals, P Fearnhead, Efficient computation of the volume of a polytope in high dimensions using Piecewise Deterministic Markov Processes, ArXiv Preprint, 2202.09129, (2022).
https://proceedings.mlr.press/v151/chevallier22a/chevallier22a.pdf
[27] J Skilling, Bayesian Computation in big spaces-nested sampling and Galilean Monte Carlo, AIP Conference Proceedings 1443, 145, (2012).
https://doi.org/10.1063/1.3703630
[28] M Griffiths, D J Wales, Nested Basin Sampling, J. Chem. Theory Comput. 15(12), 6881, (2019).
https://doi.org/10.1021/acs.jctc.9b00567
[29] S F Edwards, R B S Oakeshott, Theory of Powders, Physica A 157(3), 1080, (1989).
https://doi.org/10.1016/0378-4371(89)90034-4
[30] A Baule, F Morone, H J Herrmann, et al., Edwards statistical mechanics for jammed granular matter, Rev. Mod. Phys. 90(1), 015006, (2018).
https://doi.org/10.1103/RevModPhys.90.015006
[31] T Aste, Volume fluctuations and geometrical constraints in granular packs, Phys. Rev. Lett. 96(1), 018002, (2006).
https://doi.org/10.1103/PhysRevLett.96.018002
[32] T Aste, T Di Matteo Emergence of Gamma distributions in granular materials and packing models, Phys. Rev. E 77(2), 021309, (2008).
https://doi.org/10.1103/PhysRevE.77.021309
[33] S McNamara, P Richard, S K De Richter, et al., R Delannay Measurement of granular entropy, Phys. Rev. E 80(3), 031301, (2009).
https://doi.org/10.1103/PhysRevE.80.031301
[34] J G Puckett, K E Daniels Equilibrating temperature-like variables in jammed granular subsystems, Phys. Rev. Lett. 110(5), 058001, (2013).
https://doi.org/10.1103/PhysRevLett.110.058001
[35] S-C Zhao, M Schr ̈oter, Measuring the configurational entropy of a binary disc packing, Soft Matter 10(23), 4208, (2014).
https://doi.org/10.1039/c3sm53176g
[36] E S Bililign, J E Kollmer, K E Daniels Protocol dependence and state variables in the force-moment ensemble, Phys. Rev. Lett. 122(3), 038001, (2019).
https://doi.org/10.1103/PhysRevLett.122.038001
[37] X Sun, W Kob, R Blumenfeld, et al., Friction-controlled entropy stability competition in granular systems, Phys. Rev. Lett. 125(26), 268005, (2020).
https://doi.org/10.1103/PhysRevLett.125.268005
[38] Y Yuan, Y Xing, J Zheng, et al., Experimental test of the Edwards volume ensemble for tapped granular packings, Phys. Rev. Lett. 127(1), 018002, (2021).
https://doi.org/10.1103/PhysRevLett.127.018002
[39] J D Weeks, D Chandler, H C Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, 5237, (1971).
https://doi.org/10.1063/1.1674820
[40] C P Goodrich, S Dagois-Bohy, B P Tighe, et al., Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling, Phys. Rev. Lett. 112(14), 145502, (2014).
https://doi.org/10.1103/PhysRevE.90.022138
[41] S Atkinson, F Stillinger, S Torquato, Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings, Phys. Rev. E 88(6), 062208, (2013).
https://doi.org/10.1103/PhysRevE.88.062208
[42] G-J Gao, J Blawzdziewicz, C S O'Hern, Frequency distribution of mechanically stable disk packings, Phys. Rev. E 74, 061304, (2006).
https://doi.org/10.1103/PhysRevE.74.061304
[43] M Parrinello, A Rahman, Crystal Structure and Pair Potentials: A Molecular-Dynamics Study, Phys. Rev. Lett. 45, 413, (1980).
https://doi.org/10.1103/PhysRevLett.45.1196
[44] M Parrinello, A Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, J. App. Phys. 52, 7182, (1981).
https://doi.org/10.1063/1.328693
[45] M Parrinello, A Rahman, Strain fluctuations and elastic constants, J. Chem. Phys. 76, 2662, (1982).
https://doi.org/10.1063/1.443248
[46] R Najafabadi, S Yip, Observation of Finite Temperature Bain Transformation (f.c.c. ↔ b.c.c.) in Monte Carlo Simulation of Iron, Scr. Metall. 17, 1199, (1983).
https://doi.org/10.1016/0036-9748(83)90283-1
[47] S Yashonath, C Rao, A monte carlo study of crystal structure transformations, Mol. Phys. 54, 245, (1985).
https://doi.org/10.1080/00268978500100201
[48] R J N Baldock, L B P ́artay, A P Bart ́ok, et al., Determining pressure-temperature phase diagrams of materials, Phys. Rev. B 93, 174108, (2016).
https://doi.org/10.1103/PhysRevB.93.174108
[49] R J N Baldock, N Bernstein, K Michael Salerno, et al., Constant-pressure nested sampling with atomistic dynamics, Phys. Rev. E 96, 043311, (2017).
https://doi.org/10.1103/PhysRevE.96.043311
[50] C Anzivino, M Casiulis, T Zhang, et al., Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding, J. Chem. Phys., In Press (2022).
https://doi.org/10.1063/5.0137111
[51] T Castellani, A Cavagna, Spin-glass theory for pedestrians, J. Stat. Mech. 2005, P05012, (2005).
https://doi.org/10.1088/1742-5468/2005/05/P05012
[52] V Ros, G Ben Arous, G Biroli, et al., Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions, Phys. Rev. X 9(1), 011003, (2019).
https://doi.org/10.1103/PhysRevX.9.011003
[53] T Rizzo, Path integral approach unveils role of complex energy landscape for activated dynamics of glassy systems, Phys. Rev. B 104, 094203, (2021).
https://doi.org/10.1103/PhysRevB.104.094203
[54] G Folena, A Manacorda, F Zamponi, Introduction to the dynamics of disordered systems: equilibrium and gradient descent, Lectures Notes for the Fundamental Problems in Statistical Physics XV Summer School (2021).
https://doi.org/10.1016/j.physa.2022.128152
[55] V Ros, G Biroli, C Cammarota, Complexity of energy barriers in mean-field glassy systems, EPL 126, 20003, (2019).
https://doi.org/10.1209/0295-5075/126/20003
[56] V Ros, G Biroli, C Cammarota, Dynamical Instantons and Activated Processes in Mean-Field Glass Models, SciPost Phys. 10, 002, (2021).
https://doi.org/10.21468/SciPostPhys.10.1.002
[57] B Lacroix-à-chez-Toine, Y Fyodorov, Counting equilibria in a random non-gradient dynamics with heterogeneous relaxation rates, J. Phys. A: Math. Theor. 55, 144001, (2022).
https://doi.org/10.1088/1751-8121/ac564a
[58] J Kent-Dobias, J Kurchan, Complex complex landscapes, Phys. Rev. Research 3, 023064, (2021).
https://doi.org/10.1103/PhysRevResearch.3.023064
[59] E Bitzek, P Koskinen, F G ̈ahler, et al., Structural relaxation made simple, Phys. Rev. Lett. 97(17), 170201, (2006).
https://doi.org/10.1103/PhysRevLett.97.170201
[60] F H Stillinger, T A Weber, Hidden structure in liquids, Phys. Rev. A 25(2), 978, (1982).
https://doi.org/10.1103/PhysRevA.25.978
[61] S D Cohen, A C Hindmarsh, P F Dubois, CVODE, a stiff/nonstiff ODE solver in C, Computers in Physics 10(2), 138, (1996).
https://doi.org/10.1063/1.4822377
[62] P Charbonneau, J Kurchan, G Parisi, et al., Glass and jamming transitions: From exact results to finite-dimensional descriptions, Ann. Rev. Cond. Mat. Phys. 8(1), 265, (2017).
https://doi.org/10.1146/annurev-conmatphys-031016-025334
[63] S Franz, G Parisi, Recipes for metastable states in spin glasses, Journal de Physique I 5(11), 1401, (1995).
https://doi.org/10.1051/jp1:1995201
[64] G Parisi, F Zamponi, Mean-field theory of hard sphere glasses and jamming, Rev. Mod. Phys. 82(1), 789, (2010).
https://doi.org/10.1103/RevModPhys.82.789
[65] L Berthier, M Ozawa, C Scalliet, Configurational entropy of glass-forming liquids, J. Chem. Phys. 150(16), 160902, (2019).
https://doi.org/10.1063/1.5091961
[66] C Rulquin, P Urbani, G Biroli, et al., Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back, J. Stat. Mech. 2016(2), 023209, (2016).
https://doi.org/10.1088/1742-5468/2016/02/023209
[67] F H Stillinger, A topographic view of supercooled liquids and glass formation, Science 267(5206), 1935, (1995).
https://doi.org/10.1126/science.267.5206.1935
[68] F Sciortino, Potential energy landscape description of supercooled liquids and glasses, J. Stat. Mech. 2005(5), P05015, (2005).
https://doi.org/10.1088/1742-5468/2005/05/P05015
[69] L Berthier, P Charbonneau, D Coslovich, et al., Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling, Proc. Nat. Ac. Sci. 114(43), 11356, (2017).
https://doi.org/10.1073/pnas.1706860114
[70] M Ozawa, G Parisi, L Berthier, Configurational entropy of polydisperse supercooled liquids, J. Chem. Phys. 149(15), 154501, (2018).
https://doi.org/10.1063/1.5040975
[71] Y Nishikawa, M Ozawa, A Ikeda, et al., Relaxation Dynamics in the Energy Landscape of Glass-Forming Liquids, Phys. Rev. X 12, 021001, (2022).
https://doi.org/10.1103/PhysRevX.12.021001
[72] C Scalliet, B Guiselin, L Berthier, Excess wings and asymmetric relaxation spectra in a facilitated trap model, J. Chem. Phys. 155, 064505, (2021).
https://doi.org/10.1063/5.0060408
[73] B Guiselin, C Scalliet, L Berthier, Microscopic origin of excess wings in relaxation spectra of supercooled liquids, Nat. Phys. 18, 468, (2022).
https://doi.org/10.1038/s41567-022-01508-z
[74] A Chakraborty, P Seiler, G J Balas, Susceptibility of F/A-18 flight controllers to the fallingleaf mode: Nonlinear analysis, J. Guid. Control Dyn. 34(1), 73, (2011).
https://doi.org/10.1016/j.nonrwa.2011.06.007
[75] M Kac, On the average number of real roots of a random algebraic equation, Bull. Am. Math. Soc. 49(4), 314, (1943).
https://doi.org/10.1090/S0002-9904-1943-07912-8
[76] K Farahmand, On the average number of real roots of a random algebraic equation, Ann. Probab. 14(2), 702, (1986).
https://doi.org/10.1214/aop/1176992539
[77] E Bogomolny, O Bohigas, P Leboeuf, Distribution of roots of random polynomials, Phys. Rev. Lett. 68(18), 2726, (1992).
https://doi.org/10.1103/PhysRevLett.68.2726
[78] A Edelman, E Kostlan, How many zeros of a random polynomial are real?, Bull. Am. Math. Soc. 32(1), 1, (1995).
https://doi.org/10.1090/S0273-0979-1995-00571-9
[79] J M Rojas, On the average number of real roots of certain random sparse polynomial systems, Lectures in Applied Mathematics American Mathematical Society 32, 689, (1996).
https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=3fd6e1f2602681f0761b6e227da7984e1d5a60d5
[80] Y V Fyodorov, Complexity of random energy landscapes, glass transition, and absolute value of the spectral determinant of random matrices, Phys. Rev. Lett. 92(24), 240601, (2004).
https://doi.org/10.1103/PhysRevLett.92.240601
[81] G Malajovich, J M Rojas, High probability analysis of the condition number of sparse polynomial systems, Theor. Comput. Sci. 315(2-3), 525, (2004).
https://doi.org/10.1016/j.tcs.2004.01.006
[82] J-M Aza ̈ıs, M Wschebor, On the roots of a random system of equations. The theorem of Shub and Smale and some extensions, Found. Comput. Math. 5(2), 125, (2005).
https://doi.org/10.1007/s10208-004-0119-0
[83] D Armentano, M Wschebor, Random systems of polynomial equations. The expected number of roots under smooth analysis, Bernoulli 15(1), 249, (2009).
https://doi.org/10.3150/08-BEJ149
[84] Y V Fyodorov, G A Hiary, J Keating, Freezing transition, characteristic polynomials of random matrices, and the Riemann zeta function, Phys. Rev. Lett. 108(17), 170601, (2012).
https://doi.org/10.1103/PhysRevLett.108.170601
[85] Y V Fyodorov, C Nadal, Critical behavior of the number of minima of a random landscape at the glass transition point and the Tracy-Widom distribution, Phys. Rev. Lett. 109(16), 167203, (2012).
https://doi.org/10.1103/PhysRevLett.109.167203
[86] Y V Fyodorov, High-dimensional random fields and random matrix theory, ArXiv Preprint, arXiv:1307.2379, (2013).
https://doi.org/10.48550/arXiv.1307.2379
[87] Y V Fyodorov, A Lerario, E Lundberg, On the number of connected components of random algebraic hypersurfaces, J. Geom. Phys. 95, 1, (2015).
https://doi.org/10.1016/j.geomphys.2015.04.006
[88] D Cheng, A Schwartzman, On the explicit height distribution and expected number of local maxima of isotropic Gaussian random fields, ArXiv Preprint, arXiv:1503.01328, (2015).
https://doi.org/10.48550/arXiv.1503.01328
[89] F Krzakala, J Kurchan, Landscape analysis of constraint satisfaction problems, Phys. Rev. E 76, 021122, (2007).
https://doi.org/10.1103/PhysRevE.76.021122
[90] F Krzakala, L Zdeborov ́a, Hiding Quiet Solutions in Random Constraint Satisfaction Problems, Phys. Rev. Lett. 102, 238701, (2009).
https://doi.org/10.1103/PhysRevLett.102.238701
[91] L Zdeborov ́a, M M ́ezard, Constraint Satisfaction Problems with Isolated Solutions are Hard, J. Stat. Mech. 2008, P12004, (2008).
https://doi.org/10.1088/1742-5468/2008/12/P12004
[92] M-H Tayarani-Narajan, A Pr ̈ugel-Bennett, On the Landscape of Combinatorial Optimisation Problems, IEEE Transactions on Evolutionary Computation 18(3), 420, (2013).
https://doi.org/10.1109/TEVC.2013.2281502
[93] T C Bachlechner, K Eckerle, O Janssen, et al., Axion landscape cosmology, Journal of Cosmology and Astroparticle Physics 2019, 062, (2019).
https://doi.org/10.1088/1475-7516/2019/09/062
[94] A J Lotka, Contribution to the Theory of Periodic Reaction, J. Phys. Chem. 14(3), 271, (1910).
https://doi.org/10.1021/j150111a004
[95] A J Lotka, Analytical Note on Certain Rhythmic Relations in Organic Systems, Proc.Natl. Acad. Sci. U.S.A. 6(7), 410, (1920).
https://doi.org/10.1073/pnas.6.7.410
[96] V Volterra, Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Mem. Acad. Lincei Roma 2, 31, (1926);
Nature \textbf{118}, 558 (1926).
[97] G Bunin, Ecological communities with Lotka-Volterra dynamics, Phys. Rev. E 95(4), 042414, (2017).
https://doi.org/10.1103/PhysRevE.95.042414
[98] G Biroli, G Bunin, C Cammarota, Marginally stable equilibria in critical ecosystems, New J. Phys. 20, 083051, (2018).
https://doi.org/10.1088/1367-2630/aada58
[99] F Roy, G Biroli, G Bunin, et al., Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka-Volterra model of ecosystems, J. Phys. A: Math. Theor. 52, 484001, (2019).
https://doi.org/10.1088/1751-8121/ab1f32
[100] A Altieri, F Roy, C Cammarota, et al., Properties of Equilibria and Glassy Phases of the Random Lotka-Volterra Model with Demographic Noise, Phys. Rev. Lett. 126, 258301, (2021).
https://doi.org/10.1103/PhysRevLett.126.258301
[101] M Barbier, J-F Arnoldi, G Bunin, et al., Generic assembly patterns in complex ecological communities, Proc. Natl. Acad. Sci. U.S.A. 115(9), 2156, (2018).
https://doi.org/10.1073/pnas.1710352115
[102] G Bunin, Directionality and community-level selection, Oikos 130(4), 489, (2018).
https://doi.org/10.1111/oik.07214
[103] M Barbier, C de Mazancourt, M Loreau, et al., Fingerprints of High-Dimensional Coexistence in Complex Ecosystems, Phys. Rev. X 11(1), 011009, (2021).
https://doi.org/10.1103/PhysRevX.11.011009
[104] A J Ballard, R Das, S Martiniani, et al., Energy landscapes for machine learning, Phys. Chem. Chem. Phys. 19, 12585-12603, (2017).
https://doi.org/10.1039/C7CP01108C
[105] S Hochreiter, J Schmidhuber, Simplifying neural nets by discovering flat minima, NeurIPS 7(1994).
https://proceedings.neurips.cc/paper/1994/file/01882513d5fa7c329e940dda99b12147-Paper.pdf
[106] S Hochreiter, J Schmidhuber, Flat minima, Neur. Comput. 9(1), 1, (1997).
https://doi.org/10.1162/neco.1997.9.1.1
[107] C Baldassi, F Pittorino, R Zecchina, Shaping the learning landscape in neural networks around wide flat minima, Proc. Natl. Acad. Sci. U.S.A. 117(1), 161, (2020).
https://doi.org/10.1073/pnas.1908636117
[108] Y Feng, Y Tu, The inverse variance-flatness relation in stochastic gradient descent is critical for finding flat minima, Proc. Natl. Acad. Sci. U.S.A. 118(9), e2015617118, (2021).
https://doi.org/10.1073/pnas.2015617118
[109] S Zhang, I Reid, G P ́erez, et al., Why Flatness Correlates With Generalization For Deep Neural Networks, Arxiv Preprint arXiv:2103.06219, (2021).
https://doi.org/10.48550/arXiv.2103.06219
[110] F Pittorino, C Lucibello, C Feinauer, et al., Entropic gradient descent algorithms and wide flat minima, J. Stat. Mech. 2021, 124015, (2021).
https://doi.org/10.1088/1742-5468/ac3ae8
[111] S S Mannelli, G Biroli, C Cammarota, et al., Complex dynamics in simple neural networks: Understanding gradient flow in phase retrieval, NeurIPS 33, 3265, (2020).
https://proceedings.neurips.cc/paper/2020/file/2172fde49301047270b2897085e4319d-Paper.pdf
[112] D M Ceperley, M Dewing, The penalty method for random walks with uncertain energies, J. Chem. Phys. 110(20), 9812, (1999).
https://doi.org/10.1063/1.478034
[113] R L Stratonovich, On a Method of Calculating Quantum Distribution Functions, Soviet Physics Doklady 2, 416, (1957).
[114] J Hubbard, Calculation of Partition Functions, Phys. Rev. Lett. 3, 77, (1959).
https://doi.org/10.1103/PhysRevLett.3.77
[115] P Attard, Thermodynamics and statistical mechanics: equilibrium by entropy maximisation, Academic Press, London (2002).
[116] J W Gibbs, Elementary principles in statistical mechanics, Charles Scribner's Sons, New York (1902).
[117] M Kardar, Statistical Physics of Particles, Cambridge University Press, Cambridge (2007).
https://doi.org/10.1017/CBO9780511815898
[118] S Carnot, Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance, Annales Scientifiques de I'É.N.S., Bachelier (1824).
[119] S Martiniani, On the complexity of energy landscapes: algorithms and a direct test of the Edwards conjecture, University of Cambridge, Cambridge (2017).
https://doi.org/10.17863/CAM.12772
[120] T M Cover, Elements of information theory, John Wiley & Sons, New York (1999).
[121] D Frenkel, B Smit, Understanding molecular simulation: from algorithms to applications, Vol. I, Elsevier (2001).
[122] D Landau, K Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Second Edition, Cambridge University Press, Cambridge (2005).
https://doi.org/10.1017/CBO9780511614460
[123] D Wales, Energy landscapes: Applications to clusters, biomolecules and glasses, Cambridge University Press, Cambridge (2003).
[124] F H Stillinger, Energy landscapes, inherent structures, and condensed-matter phenomena, Princeton University Press, New Yersey (2015).
https://doi.org/10.2307/j.ctvc77g0v
[125] E Kostlan, On the expected number of real roots of a system of random polynomial equations, Foundations of Computational Mathematics, World Scientific, Singapore (2002).
https://doi.org/10.1142/9789812778031_0007
[126] A J Lotka, Elements of Physical Biology, Williams and Wilkins, Baltimore (1925).
[127] S Artstein-Avidan, A Giannopoulos, V D Milman, Asymptotic Geometric Analysis, Part I, Mathematical Surveys and Monographs, Volume 202, American Mathematical Society, Providence, Rhode Island (2015).
https://doi.org/10.1090/surv/202
[128] I Gel'Fand, G Shilov, Generalized functions, Vol. 1, Academic Press, New York (1968).
https://doi.org/10.1016/B978-1-4832-2977-5.50005-3
[129] E W Weisstein, Gabriel's Horn, In: MathWorld-A Wolfram Web Resource, mathworld.wolfram.com/GabrielsHorn.html.
mathworld.wolfram.com/GabrielsHorn.html
[130] D Frenkel, Private communication.