49. Empirical validation of the polarization transition in a double-random field model of elections
Jan Korbel, Remah Dahdoul, Stefan Thurner
Physical Review Letters 137 (2026) 127402.
doi: 10.1103/9gjj-1df6
48. What does it mean for a system to compute?
David Wolpert, Jan Korbel
Journal of Physics: Complexity 7 (2026) 015010.
doi: 10.1088/2632-072X/ae3af8
47. Reply to Völker et al.: On the evidence of increased close friendships in societies
Stefan Thurner, Markus Hofer, Jan Korbel
PNAS 123(7) (2026) e2535183123.
doi: 10.1073/pnas.2535183123
46. Why more social interactions lead to more polarization in societies
Stefan Thurner, Markus Hofer, Jan Korbel
PNAS 122(44) (2025) e2517530122
doi: 10.1073/pnas.2517530122
45. Microscopic origin of abrupt mixed-order phase transitions
Jan Korbel, Shlomo Havlin, Stefan Thurner
Nature Communications 16 (2025)2628
doi: 10.1038/s41467-025-57007-1
44. Is stochastic thermodynamics the key to understanding the energy costs of computation?
David Wolpert, Jan Korbel, Christopher Lynn, Farita Tasnim, Joshua Grochow, Gülce Kardeş, James Aimone, Vijay Balasubramanian, Eric de Giuli, David Doty, Nahuel Freitas, Matteo Marsili, Thomas E. Ouldridge, Andrea Richa, Paul Riechers, Édgar Roldán, Brenda Rubenstein, Zoltan Toroczkai, Joseph Paradiso
PNAS121(45) (2024) e2321112121
doi: 10.1073/pnas.2321112121
43. Nonequilibrium thermodynamics of uncertain stochastic processes
Jan Korbel, David Wolpert
Physical Review Research 6 (2024) 013021
doi: 10.1103/PhysRevResearch.6.013021
42. A large-scale empirical investigation of specialization in criminal career
Georg Heiler, Tuan Pham Minh, Jan Korbel, Johannes Wachs, Stefan Thurner
Scientific Reports 13 (2023) 17160
doi: 10.1038/s41598-023-43552-6
41. Thermodynamics of exponential Kolmogorov-Nagumo averages
Pablo A. Morales, Jan Korbel, Fernando E. Rosas
New Journal of Physics 25 (2023) 073011
doi: 10.1088/1367-2630/ACE4EB
40. Geometric Structures Induced by Deformations of the Legendre Transform
Pablo A. Morales, Jan Korbel, Fernando E. Rosas
Entropy 25(4) (2023) 678
doi: 10.3390/E25040678
39. Homophily-Based Social Group Formation in a Spin Glass Self-Assembly Framework
Jan Korbel, Simon D. Lindner, Tuan Pham, Rudolf Hanel, Stefan Thurner
Physical Review Letters 130 (2023) 057401
doi: 10.1103/PhysRevLett.130.057401
38. Energy distribution of inelastic gas in a box is dominated by a power law – a derivation in the framework of sample space reducing processes
Stefan Thurner, Jan Korbel, Rudolf Hanel
New Journal of Physics 25 (2023) 013014
doi: 10.1088/1367-2630/ACAF15
37. Empirical social triad statistics can be explained with dyadic homophylic interactions
Tuan Pham Minh, Jan Korbel, Rudolf Hanel, Stefan Thurner
PNAS 119 (6) (2022) e2121103119
doi: 10.1073/pnas.2121103119
36. On the Quantitative Properties of Some Market Models Involving Fractional Derivatives
Jean-Philippe Aguilar, Jan Korbel, Nicolas Pesci
Mathematics 9(24) (2021) 3198
doi: 10.3390/math9243198
35. The Statistical Foundations of Entropy
Petr Jizba, Jan Korbel
Entropy 23(10) (2021) 1367
doi: 10.3390/e23101367
34. Balance and fragmentation in societies with homophily and social balance
Tuan Pham Minh, Andrew C. Alexander, Jan Korbel, Rudolf Hanel, Stefan Thurner
Scientific Reports 11 (2021) 17188
doi: 10.1038/S41598-021-96065-5
33. Stochastic thermodynamics and fluctuation theorems for non-linear systems
Jan Korbel, David Wolpert
New Journal of Physics 23 (2021) 033049
doi: 10.1088/1367-2630/ABEA46
32. An overview of generalized entropic forms
Velimir Ilic, Jan Korbel, Shamik Gupta, Antonio Maria Scarfone
Europhysics Letters 133 (2021) 50005
doi: 10.1209/0295-5075/133/50005
31. Thermodynamics of structure-forming systems
Jan Korbel, Simon D. Lindner, Rudolf Hanel, Stefan Thurner
Nature Communications 12 (2021) 1127
doi: 10.1038/S41467-021-21272-7
30. Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle
Jan Korbel
Entropy 23(1) (2021) 96
doi: 10.3390/E23010096
29. Pricing, Risk and Volatility in Subordinated Market Models
Jean-Philippe Aguilar, Justin Lars Kirkby, Jan Korbel
Risks 8(4) (2020) 124
doi: 10.3390/risks8040124
28. A structured open dataset of government interventions in response to COVID-19
Amelie Desvars-Larrive et al.
Scientific Data 7 (2020) 285
doi: 10.1038/S41597-020-00609-9
27. Applications of Hilfer-Prabhakar Operator to Option Pricing Financial Model
Živorad Tomovski, Johan L. A. Dubbeldam, Jan Korbel
Fractional Calculus and Applied Analysis 23 (2020) 996–1012
doi: 10.1515/FCA-2020-0052
26. When Shannon and Khinchin meet Shore and Johnson: Equivalence of information theory and statistical inference axiomatics
Petr Jizba, Jan Korbel
Physical Review E 101 (2020) 042126
doi: 10.1103/PhysRevE.101.042126
25. Information geometry of scaling expansions of non-exponentially growing configuration spaces
Jan Korbel, Rudolf Hanel, Stefan Thurner
European Physical Journal Special Topics 229 (2020) 787–807
doi: 10.1140/epjst/e2020-900190-x
24. Predicting collapse of adaptive networked systems without knowing the network
Leonhard Horstmeyer, Tuan Pham Minh, Jan Korbel, Stefan Thurner
Scientific Reports 10 (2020) 1223
doi: 10.1038/s41598-020-57751-y
23. Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model
Jean-Philippe Aguilar, Jan Korbel
Risks 7(2) (2019) 36
doi: 10.3390/risks7020036
22. Information Geometric Duality of phi-Deformed Exponential Families
Jan Korbel, Rudolf Hanel, Stefan Thurner
Entropy 21(2) (2019) 112
doi:10.3390/e21020112
21. Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations
Jean-Philippe Aguilar, Jan Korbel, Yuri Luchko
Mathematics 7(9) (2019) 796
doi:10.3390/math7090796
20. Maximum Entropy Principle in Statistical Inference: Case for Non-Shannonian Entropies
Petr Jizba, Jan Korbel
Physical Review Letters 122 (2019) 120601
doi: 10.1103/PhysRevLett.122.120601
19. Comment on „Renyi entropy yields artificial biases not in the data and incorrect updating due to the finite size data“
Petr Jizba, Jan Korbel
Physical Review E 100 (2019) 026101
doi: 10.1103/PhysRevE.100.026101
18. Transfer Entropy between Communities in Complex Financial Networks
Jan Korbel, Xiongfei Jiang, Bo Zheng
Entropy 21(11) (2019) 1124
doi: 10.3390/e21111124
17. Least informative distributions in maximum q-log-likelihood estimation
Mehmet Niyazi Cankaya, Jan Korbel
Physica A 509 (2018) 140-150
doi: 10.1016/j.physa.2018.06.004
16. Classification of complex systems by their sample-space scaling exponents
Jan Korbel, Rudolf Hanel, Stefan Thurner
New Journal of Physics 20 (2018) 093007
doi: 10.1088/1367-2630/aadcbe
15. Series representation of the pricing formula for the European option driven by space-time fractional diffusion
Jean-Philippe Aguilar, Cyril Coste, Jan Korbel
Fractional Calculus and Applied Analysis 21 (2018) 981–1004
doi: 10.1515/fca-2018-0054
14. Transitions between superstatistical regimes: Validity, breakdown and applications
Petr Jizba, Jan Korbel, Hynek Lavička, Martin Prokš, Václav Svoboda, Christian Beck
Physica A 493 (2018) 29-46
doi: 10.1016/j.physa.2017.09.109
13. Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications
Jean-Philippe Aguilar, Jan Korbel
Fractal and Fractional 2(1) (2018) 15
doi: 10.3390/fractalfract2010015
12. Point Divergence Gain and Multidimensional Data Sequences Analysis
Renata Rychtáriková, Jan Korbel, Petr Macháček, Dalibor Štys
Entropy 20(2) (2018) 106
doi: 10.3390/e2002010
11. On the Uniqueness Theorem for Pseudo-Additive Entropies
Petr Jizba, Jan Korbel
Entropy 19(11) (2018) 605
doi: 10.3390/e19110605
10. Rescaling the nonadditivity parameter in Tsallis thermostatistics
Jan Korbel
Physics Letters A 381(32) (2017) 2588-2592
doi: 10.1016/j.physleta.2017.06.033
9. On statistical properties of Jizba-Arimitsu hybrid entropy
Jan Korbel
Physica A 475 (2017) 1-10
doi: 10.1016/j.physa.2017.02.009
8. Tsallis thermostatics as a statistical physics of random chains
Petr Jizba, Jan Korbel, and Václav Zatloukal
Physical Review E 95 (2017) 022103
doi: 10.1103/PhysRevE.95.022103
7. Remarks on „Comments on ‚On q-non-extensive statistics with non-Tsallisian entropy‘ “ [Physica A 466 (2017) 160]
Petr Jizba, Jan Korbel
Physica A 468 (2017) 238-243
doi: 10.1016/j.physa.2016.11.006
6. Point Information Gain and Multidimensional Data Analysis
Renata Rychtáriková, Jan Korbel, Petr Macháček, Petr Císař, Jan Urban, Dalibor Štys
Entropy 18(10) (2015) 372
doi: 10.3390/e18100372
5. Modeling of Financial Processes with A Space-Time Fractional Diffusion Equation of Varying Order
Jan Korbel, Yuri Luchko
Fractional Calculus and Applied Analysis 19 (2016) 1414–1433
doi: 10.1515/fca-2016-0073
4. Option pricing beyond Black-Scholes based on double-fractional diffusion
Hagen Kleinert, Jan Korbel
Physica A 449 (2016) 200-214
doi: 10.1016/j.physa.2015.12.125
3. On q-non-extensive statistics with non-Tsallisian entropy
Petr Jizba, Jan Korbel
Physica A 444 (2016) 808-827
doi: 10.1016/j.physa.2015.10.084
2. Techniques for multifractal spectrum estimation in financial time series
Petr Jizba, Jan Korbel
International Journal of Design & Nature and Ecodynamics 10 (2015) 261-266+0.3390/fractalfract2010015
doi: 10.2495/DNE-V10-N3-261-266
1. Multifractal diffusion entropy analysis: Optimal bin width of probability histograms
Petr Jizba, Jan Korbel
Physica A 413 (2014) 438-458+0.3390/fractalfract2010015
doi: 10.1016/j.physa.2014.07.008