Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport

[1]  Shuntaro Sasai,et al.  Optimal Control Costs of Brain State Transitions in Linear Stochastic Systems , 2022, The Journal of Neuroscience.

[2]  T. Sagawa,et al.  Thermodynamic uncertainty relations for steady-state thermodynamics. , 2022, Physical review. E.

[3]  Jumpei F. Yamagishi,et al.  Geometric speed limit for acceleration by natural selection in evolutionary processes , 2022, Physical Review Research.

[4]  T. Vu,et al.  Topological Speed Limit. , 2022, Physical review letters.

[5]  T. Vu,et al.  Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits , 2022, Physical Review X.

[6]  Artemy Kolchinsky,et al.  Housekeeping and excess entropy production for general nonlinear dynamics , 2022, Physical Review Research.

[7]  Grant M. Rotskoff,et al.  Unified, Geometric Framework for Nonequilibrium Protocol Optimization. , 2022, Physical review letters.

[8]  Wuchen Li,et al.  Wasserstein information matrix , 2019, Information Geometry.

[9]  Tetsuya J. Kobayashi,et al.  Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions , 2022, Physical Review Research.

[10]  Jun Zhang,et al.  When optimal transport meets information geometry , 2022, Information Geometry.

[11]  Artemy Kolchinsky,et al.  Information geometry of excess and housekeeping entropy production , 2022, ArXiv.

[12]  David A. Sivak,et al.  Optimal control with a strong harmonic trap. , 2022, Physical review. E.

[13]  M. Grmela,et al.  On the role of geometry in statistical mechanics and thermodynamics. II. Thermodynamic perspective , 2022, Journal of Mathematical Physics.

[14]  M. Grmela,et al.  On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective , 2022, Journal of Mathematical Physics.

[15]  H. Qian,et al.  Statistical Thermodynamics and Data ad Infinitum: Conjugate Variables as Forces, and their Statistical Variations , 2022, 2205.09321.

[16]  M. DeWeese,et al.  Limited-control optimal protocols arbitrarily far from equilibrium. , 2022, Physical review. E.

[17]  A. Prados,et al.  Thermal brachistochrone for harmonically confined Brownian particles , 2022, The European Physical Journal Plus.

[18]  C. Jarzynski,et al.  Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics , 2022, Reports on progress in physics. Physical Society.

[19]  J. S. Lee,et al.  Speed Limit for a Highly Irreversible Process and Tight Finite-Time Landauer's Bound. , 2022, Physical review letters.

[20]  T. Georgiou,et al.  Geometry of Finite-Time Thermodynamic Cycles With Anisotropic Thermal Fluctuations , 2022, IEEE Control Systems Letters.

[21]  Luis Pedro Garc'ia-Pintos Diversity and fitness uncertainty allow for faster evolutionary rates , 2022, 2202.07533.

[22]  A. Dechant,et al.  Geometric decomposition of entropy production into excess, housekeeping, and coupling parts. , 2022, Physical review. E.

[23]  Ryusuke Hamazaki,et al.  Universal constraint on nonlinear population dynamics , 2022, Communications Physics.

[24]  Sosuke Ito,et al.  Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates. , 2021, Physical review. E.

[25]  Tetsuya J. Kobayashi,et al.  Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints , 2021, Physical Review Research.

[26]  Adam G. Frim,et al.  Geometric Bound on the Efficiency of Irreversible Thermodynamic Cycles. , 2021, Physical review letters.

[27]  C. P. Sun,et al.  Geodesic Path for the Minimal Energy Cost in Shortcuts to Isothermality. , 2021, Physical review letters.

[28]  A. Dechant Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes , 2021, Journal of Physics A: Mathematical and Theoretical.

[29]  A. Dechant,et al.  Geometric decomposition of entropy production in out-of-equilibrium systems , 2021, Physical Review Research.

[30]  Sebastian Deffner,et al.  Shortcuts in stochastic systems and control of biophysical processes , 2021, bioRxiv.

[31]  H. Qian,et al.  Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations. , 2020, Physical review letters.

[32]  Ting-Kam Leonard Wong,et al.  Pseudo-Riemannian geometry encodes information geometry in optimal transport , 2019, Information geometry.

[33]  Sosuke Ito,et al.  Game-theoretical approach to minimum entropy productions in information thermodynamics , 2021, 2112.14035.

[34]  Sosuke Ito,et al.  Inferring nonequilibrium thermodynamics from tilted equilibrium using information-geometric Legendre transform , 2021, 2112.11008.

[35]  Ryusuke Hamazaki Speed Limits for Macroscopic Transitions , 2021, 2110.09716.

[36]  Diederik P. Kingma,et al.  Variational Diffusion Models , 2021, ArXiv.

[37]  O. Dahlsten,et al.  Universal Bound on Energy Cost of Bit Reset in Finite Time. , 2021, Physical review letters.

[38]  David A. Sivak,et al.  Steps minimize dissipation in rapidly driven stochastic systems. , 2021, Physical review. E.

[39]  Sosuke Ito,et al.  Thermodynamic Uncertainty Relation and Thermodynamic Speed Limit in Deterministic Chemical Reaction Networks. , 2021, Physical review letters.

[40]  S. Ito,et al.  Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance , 2021, Physical Review Research.

[41]  Gershon Wolansky,et al.  Optimal Transport , 2021 .

[42]  S. Amari Information geometry , 2021, Japanese Journal of Mathematics.

[43]  Abhishek Kumar,et al.  Score-Based Generative Modeling through Stochastic Differential Equations , 2020, ICLR.

[44]  Andreas Dechant,et al.  Continuous time reversal and equality in the thermodynamic uncertainty relation , 2020, Physical Review Research.

[45]  D. Wolpert,et al.  Entropy production and thermodynamics of information under protocol constraints , 2020, ArXiv.

[46]  Sosuke Ito,et al.  Information geometric inequalities of chemical thermodynamics , 2020, Physical Review Research.

[47]  Yoshihiko Hasegawa,et al.  Geometrical Bounds of the Irreversibility in Markovian Systems. , 2020, Physical review letters.

[48]  Tryphon T. Georgiou,et al.  Maximal power output of a stochastic thermodynamic engine , 2020, Autom..

[49]  Sosuke Ito Information geometry, trade-off relations, and generalized Glansdorff-Prigogine criterion for stability , 2019, Journal of Physics A: Mathematical and Theoretical.

[50]  Wuchen Li Transport information geometry I: Riemannian calculus on probability simplex , 2018, ArXiv.

[51]  K. Aoki,et al.  Experimental evaluation of thermodynamic cost and speed limit in living cells via information geometry , 2020, bioRxiv.

[52]  S. Frank,et al.  The Fundamental Equations of Change in Statistical Ensembles and Biological Populations , 2020, Entropy.

[53]  Shaohua Guan,et al.  Information geometry in the population dynamics of bacteria , 2020, Journal of Statistical Mechanics: Theory and Experiment.

[54]  Pieter Abbeel,et al.  Denoising Diffusion Probabilistic Models , 2020, NeurIPS.

[55]  J. Bechhoefer,et al.  Finite-Time Landauer Principle. , 2020, Physical review letters.

[56]  J. Bechhoefer,et al.  Optimal finite-time bit erasure under full control. , 2020, Physical review. E.

[57]  Wuchen Li,et al.  Hessian metric via transport information geometry , 2020, Journal of Mathematical Physics.

[58]  T. Sagawa,et al.  Estimating entropy production by machine learning of short-time fluctuating currents. , 2020, Physical review. E.

[59]  Luis Pedro García-Pintos,et al.  Time–information uncertainty relations in thermodynamics , 2020, Nature Physics.

[60]  Masahito Ueda,et al.  Thermodynamic Uncertainty Relation for Arbitrary Initial States. , 2019, Physical review letters.

[61]  K. Fujii,et al.  Nonadiabatic Control of Geometric Pumping. , 2019, Physical review letters.

[62]  Keiji Saito,et al.  Thermodynamic Geometry of Microscopic Heat Engines. , 2019, Physical review letters.

[63]  A. Dechant,et al.  Stochastic Time Evolution, Information Geometry, and the Cramér-Rao Bound , 2018, Physical Review X.

[64]  Tryphon T. Georgiou,et al.  Stochastic Control and Nonequilibrium Thermodynamics: Fundamental Limits , 2018, IEEE Transactions on Automatic Control.

[65]  A. Dechant,et al.  Thermodynamic interpretation of Wasserstein distance , 2019, 1912.08405.

[66]  Aidan I Brown,et al.  Theory of Nonequilibrium Free Energy Transduction by Molecular Machines. , 2019, Chemical reviews.

[67]  David A. Sivak,et al.  Using a system’s equilibrium behavior to reduce its energy dissipation in nonequilibrium processes , 2019, Proceedings of the National Academy of Sciences.

[68]  Keiji Saito,et al.  Information-Theoretical Bound of the Irreversibility in Thermal Relaxation Processes. , 2019, Physical review letters.

[69]  H. Hasegawa,et al.  Reconsideration of the generalized second law based on information geometry , 2019, Journal of Physics Communications.

[70]  Yoshihiko Hasegawa,et al.  Uncertainty relations in stochastic processes: An information inequality approach. , 2018, Physical review. E.

[71]  S. Amari,et al.  Unified framework for the entropy production and the stochastic interaction based on information geometry , 2018 .

[72]  Steven A. Frank,et al.  The Price Equation Program: Simple Invariances Unify Population Dynamics, Thermodynamics, Probability, Information and Inference , 2018, Entropy.

[73]  A. Dechant Multidimensional thermodynamic uncertainty relations , 2018, Journal of Physics A: Mathematical and Theoretical.

[74]  Sosuke Ito Stochastic Thermodynamic Interpretation of Information Geometry. , 2017, Physical review letters.

[75]  A. Dechant,et al.  Current fluctuations and transport efficiency for general Langevin systems , 2017, Journal of Statistical Mechanics: Theory and Experiment.

[76]  Shun-ichi Amari,et al.  Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem , 2017, Information Geometry.

[77]  Kazutaka Takahashi Shortcuts to adiabaticity applied to nonequilibrium entropy production: an information geometry viewpoint , 2017, 1708.08497.

[78]  Léon Bottou,et al.  Wasserstein Generative Adversarial Networks , 2017, ICML.

[79]  C. Jarzynski,et al.  Shortcuts to adiabaticity using flow fields , 2017, 1707.01490.

[80]  Grant M. Rotskoff,et al.  Geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems. , 2016, Physical review. E.

[81]  Sosuke Ito,et al.  Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality , 2016, Scientific Reports.

[82]  Massimiliano Esposito,et al.  Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics , 2016, 1602.07257.

[83]  Shun-ichi Amari,et al.  Information Geometry and Its Applications , 2016 .

[84]  H. Qian,et al.  Nonequilibrium thermodynamic formalism of nonlinear chemical reaction systems with Waage–Guldberg’s law of mass action , 2016, 1601.03158.

[85]  Todd R. Gingrich,et al.  Dissipation Bounds All Steady-State Current Fluctuations. , 2015, Physical review letters.

[86]  Shun-ichi Amari,et al.  Unified framework for information integration based on information geometry , 2015, Proceedings of the National Academy of Sciences.

[87]  Tryphon T. Georgiou,et al.  On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint , 2014, J. Optim. Theory Appl..

[88]  Christopher Jarzynski,et al.  Analysis of slow transitions between nonequilibrium steady states , 2015, 1507.06269.

[89]  Udo Seifert,et al.  Thermodynamic uncertainty relation for biomolecular processes. , 2015, Physical review letters.

[90]  T. Sagawa,et al.  Thermodynamics of information , 2015, Nature Physics.

[91]  C. Maes,et al.  Revisiting the Glansdorff–Prigogine Criterion for Stability Within Irreversible Thermodynamics , 2014, 1410.2183.

[92]  Jordan M. Horowitz,et al.  Thermodynamics with Continuous Information Flow , 2014, 1402.3276.

[93]  A. C. Barato,et al.  Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell’s demon interpretation , 2014, 1402.0419.

[94]  C. Maes,et al.  A Nonequilibrium Extension of the Clausius Heat Theorem , 2012, 1206.3423.

[95]  Christian L'eonard A survey of the Schr\"odinger problem and some of its connections with optimal transport , 2013, 1308.0215.

[96]  K. Dill,et al.  Principles of maximum entropy and maximum caliber in statistical physics , 2013 .

[97]  Sosuke Ito,et al.  Information thermodynamics on causal networks. , 2013, Physical review letters.

[98]  U. Seifert Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[99]  David A. Sivak,et al.  Thermodynamic metrics and optimal paths. , 2012, Physical review letters.

[100]  Erik Aurell,et al.  Refined Second Law of Thermodynamics for Fast Random Processes , 2012, Journal of Statistical Physics.

[101]  T. Sagawa,et al.  Geometrical expression of excess entropy production. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[102]  J. Maas Gradient flows of the entropy for finite Markov chains , 2011, 1102.5238.

[103]  Paolo Muratore-Ginanneschi,et al.  Optimal protocols and optimal transport in stochastic thermodynamics. , 2010, Physical review letters.

[104]  M. Esposito,et al.  Three faces of the second law. II. Fokker-Planck formulation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[105]  M. Esposito,et al.  Three faces of the second law. I. Master equation formulation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[106]  C. Villani Optimal Transport: Old and New , 2008 .

[107]  S. Sasa,et al.  Steady-state thermodynamics for heat conduction: microscopic derivation. , 2007, Physical review letters.

[108]  Gavin E Crooks,et al.  Measuring thermodynamic length. , 2007, Physical review letters.

[109]  C. Jarzynski,et al.  Path-integral analysis of fluctuation theorems for general Langevin processes , 2006, cond-mat/0605471.

[110]  C. Villani Topics in Optimal Transportation , 2003 .

[111]  H. Qian Entropy production and excess entropy in a nonequilibrium steady-state of single macromolecules. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[112]  T. Hatano,et al.  Steady-state thermodynamics of Langevin systems. , 2000, Physical review letters.

[113]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[114]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[115]  Yann Brenier,et al.  A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , 2000, Numerische Mathematik.

[116]  G. Crooks Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[117]  Hans Christian Öttinger,et al.  General projection operator formalism for the dynamics and thermodynamics of complex fluids , 1998 .

[118]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. I. Development of a general formalism , 1997 .

[119]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism , 1997 .

[120]  A. Beghi,et al.  On the relative entropy of discrete-time Markov processes with given end-point densities , 1996, IEEE Trans. Inf. Theory.

[121]  D. Kinderlehrer,et al.  THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .

[122]  George Ruppeiner,et al.  Riemannian geometry in thermodynamic fluctuation theory , 1995 .

[123]  W. Ebeling Stochastic Processes in Physics and Chemistry , 1995 .

[124]  J. G. Koller,et al.  Adiabatic Switching, Low Energy Computing, And The Physics Of Storing And Erasing Information , 1992, Workshop on Physics and Computation.

[125]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[126]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[127]  Michael I. Jordan,et al.  Advances in Neural Information Processing Systems 30 , 1995 .

[128]  Peter Salamon,et al.  Thermodynamic length and dissipated availability , 1983 .

[129]  G. Ruppeiner,et al.  Thermodynamics: A Riemannian geometric model , 1979 .

[130]  J. Schnakenberg Network theory of microscopic and macroscopic behavior of master equation systems , 1976 .

[131]  Frank Weinhold,et al.  Metric geometry of equilibrium thermodynamics , 1975 .

[132]  I Prigogine,et al.  The thermodynamic stability theory of non-equilibrium States. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[133]  H. Callen Thermodynamics and an Introduction to Thermostatistics , 1988 .

[134]  Albert Einstein,et al.  Investigations on the Theory of the Brownian Movement , 1928, The Mathematical Gazette.

[135]  L. Onsager Reciprocal Relations in Irreversible Processes. II. , 1931 .

[136]  October I Physical Review Letters , 2022 .