Max Welling is the co-founder and Chief Technology Officer of the startup CuspAI, and a Full Professor of Machine Learning at the University of Amsterdam. He is a member of the Dutch Royal Academy of Sciences and the Canadian Institute for Advanced Research, and a fellow of the European Lab for Learning and Intelligent Systems. Professor Welling received the ECCV Koenderink Prize in 2010, the 2021 ICML Test of Time Award, and the 2024 ICLR Test of Time Award. Sirui Lu is a doctoral researcher at the Max Planck Institute of Quantum Optics, Germany. His research focuses on the intersection of (quantum) physics and artificial intelligence. He previously earned his master's and bachelor's degrees in physics from the Technical University of Munich and Tsinghua University, Beijing, respectively. Lars Holdijk is a PhD student at the University of Oxford. His research focuses on the intersection of generative artificial intelligence, computational biochemistry, and statistical physics.

• Preface; Acknowledgement; Why stochastic thermodynamics of machine learning?; Part I. Preliminaries: 1. Mathematical preliminaries; 2. Neural network preliminaries; 3. Physics preliminaries; Part II. Discrete-time Stochastic Dynamics:4. Latent variable models and graphical models; 5. Thermodynamics of probabilistic machine learning; 6. Belief propagation; 7. The variational autoencoder; 8. Normalizing flows; 9. Markov processes and time reversal; 10. Stochastic thermodynamics; 11. Markov chain Monte Carlo; 12. Sequential importance sampling; 13. Variational diffusion models; 14. Schro¨ dinger bridges; 15. Optimal control; 16. Generative flow networks; 17. Fluctuation theorems; 18. Free energy estimation; 19. Escorted free energy estimations and fluctuation theorems; 20. Hybrid stochastic flows and surjective flows; Part III. Continuous-time Probabilistic Dynamics: 21. Stochastic thermodynamics from the Fokker–Planck equation; 22. Optimal transport and Schro¨ dinger bridge; 23. Continuous normalizing flows and flow matching; Part IV. Epilogue: 24. Unification: free energy is all you need; Bibliography; Index.

'Just as thermodynamics proved key to understanding the age of steam, stochastic thermodynamics will prove key to understanding the age of AI. This book is the first comprehensive guide to the principles of stochastic thermodynamics and how they relate to modern AI. It is much needed and will be widely read.' Neil Lawrence, University of Cambridge

Max Welling is the co-founder and Chief Technology Officer of the startup CuspAI, and a Full Professor of Machine Learning at the University of Amsterdam. He is a member of the Dutch Royal Academy of Sciences and the Canadian Institute for Advanced Research, and a fellow of the European Lab for Learning and Intelligent Systems. Professor Welling received the ECCV Koenderink Prize in 2010, the 2021 ICML Test of Time Award, and the 2024 ICLR Test of Time Award. Sirui Lu is a doctoral researcher at the Max Planck Institute of Quantum Optics, Germany. His research focuses on the intersection of (quantum) physics and artificial intelligence. He previously earned his master's and bachelor's degrees in physics from the Technical University of Munich and Tsinghua University, Beijing, respectively. Lars Holdijk is a PhD student at the University of Oxford. His research focuses on the intersection of generative artificial intelligence, computational biochemistry, and statistical physics.

• Preface; Acknowledgement; Why stochastic thermodynamics of machine learning?; Part I. Preliminaries: 1. Mathematical preliminaries; 2. Neural network preliminaries; 3. Physics preliminaries; Part II. Discrete-time Stochastic Dynamics:4. Latent variable models and graphical models; 5. Thermodynamics of probabilistic machine learning; 6. Belief propagation; 7. The variational autoencoder; 8. Normalizing flows; 9. Markov processes and time reversal; 10. Stochastic thermodynamics; 11. Markov chain Monte Carlo; 12. Sequential importance sampling; 13. Variational diffusion models; 14. Schro¨ dinger bridges; 15. Optimal control; 16. Generative flow networks; 17. Fluctuation theorems; 18. Free energy estimation; 19. Escorted free energy estimations and fluctuation theorems; 20. Hybrid stochastic flows and surjective flows; Part III. Continuous-time Probabilistic Dynamics: 21. Stochastic thermodynamics from the Fokker–Planck equation; 22. Optimal transport and Schro¨ dinger bridge; 23. Continuous normalizing flows and flow matching; Part IV. Epilogue: 24. Unification: free energy is all you need; Bibliography; Index.

'Just as thermodynamics proved key to understanding the age of steam, stochastic thermodynamics will prove key to understanding the age of AI. This book is the first comprehensive guide to the principles of stochastic thermodynamics and how they relate to modern AI. It is much needed and will be widely read.' Neil Lawrence, University of Cambridge

Max Welling is the co-founder and Chief Technology Officer of the startup CuspAI, and a Full Professor of Machine Learning at the University of Amsterdam. He is a member of the Dutch Royal Academy of Sciences and the Canadian Institute for Advanced Research, and a fellow of the European Lab for Learning and Intelligent Systems. Professor Welling received the ECCV Koenderink Prize in 2010, the 2021 ICML Test of Time Award, and the 2024 ICLR Test of Time Award. Sirui Lu is a doctoral researcher at the Max Planck Institute of Quantum Optics, Germany. His research focuses on the intersection of (quantum) physics and artificial intelligence. He previously earned his master's and bachelor's degrees in physics from the Technical University of Munich and Tsinghua University, Beijing, respectively. Lars Holdijk is a PhD student at the University of Oxford. His research focuses on the intersection of generative artificial intelligence, computational biochemistry, and statistical physics.

• Preface; Acknowledgement; Why stochastic thermodynamics of machine learning?; Part I. Preliminaries: 1. Mathematical preliminaries; 2. Neural network preliminaries; 3. Physics preliminaries; Part II. Discrete-time Stochastic Dynamics:4. Latent variable models and graphical models; 5. Thermodynamics of probabilistic machine learning; 6. Belief propagation; 7. The variational autoencoder; 8. Normalizing flows; 9. Markov processes and time reversal; 10. Stochastic thermodynamics; 11. Markov chain Monte Carlo; 12. Sequential importance sampling; 13. Variational diffusion models; 14. Schro¨ dinger bridges; 15. Optimal control; 16. Generative flow networks; 17. Fluctuation theorems; 18. Free energy estimation; 19. Escorted free energy estimations and fluctuation theorems; 20. Hybrid stochastic flows and surjective flows; Part III. Continuous-time Probabilistic Dynamics: 21. Stochastic thermodynamics from the Fokker–Planck equation; 22. Optimal transport and Schro¨ dinger bridge; 23. Continuous normalizing flows and flow matching; Part IV. Epilogue: 24. Unification: free energy is all you need; Bibliography; Index.

'Just as thermodynamics proved key to understanding the age of steam, stochastic thermodynamics will prove key to understanding the age of AI. This book is the first comprehensive guide to the principles of stochastic thermodynamics and how they relate to modern AI. It is much needed and will be widely read.' Neil Lawrence, University of Cambridge