[1]

A. Agrachev and Y. Sachkov, Control Theory from the Geometric Viewpoint, SpringerVerlag, Berlin, 2004.
doi: 10.1007/9783662064047.

[2]

A. Agrachev, D. Barilari and U. Boscain, Introduction to Riemannian and subRiemannian geometry, 2014. Available from: https://webusers.imjprg.fr/~davide.barilari/ABBSRnotes110715.pdf.

[3]

P. Bamberg and S. Sternberg, A Course in Mathematics for Students of Physics: 2, Cambridge University Press, Cambridge, 1991.

[4]

A. M. Bloch, Nonholonomic Mechanics and Control, SpringerVerlag, New York, 2003.

[5]

M. Born, Natural Philosophy of Cause and Chance, Dover, New York, 1964.

[6]

R. W. Brockett, Control Theory and Singular Riemannian Geometry, New Directions in Applied Mathematics (eds. P. J. Hilton and G. S. Young), SpringerVerlag, (1982), New York, 11–27.

[7]

R. W. Brockett, Nonlinear control theory and differential geometry, Proceedings of the International Congress of Mathematicians (eds. Z. Ciesielski and C. Olech), Polish Scientific Publishers, (1984), Warszawa, 1357–1368.

[8]

R. W. Brockett, Control of stochastic ensembles, The Astrom Symposium on Control(eds. B. Wittenmark and A. Rantzer), Studentlitteretur, (1999), Lund, 199–216.

[9]

R. W. Brockett, Thermodynamics with time: Exergy and passivity, Systems and Control Letters, 101 (2017), 4449.
doi: 10.1016/j.sysconle.2016.06.009.

[10]

R. W. Brockett and J. C. Willems, Stochastic Control and the Second Law of Thermodynamics, Proceedings of the 17th IEEE Conference on Decision and Control, IEEE, (1978), New York, 1007–1011.
doi: 10.1109/CDC.1978.268083.

[11]

C. Bustamante, J. Liphardt and F. Ritort, The nonequilibrium thermodynamics of small systems, Physics Today, 58, 7, 43 (2005).

[12]

C. Carathéodory, Untersuchungen über die Grundlagen der Thermodynamik, Mathematische Annalen, 67 (1909), 355386.
doi: 10.1007/BF01450409.

[13]

S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover Publications, Inc., New York, N. Y. 1957.

[14]

M. Chen and C. J. Tomlin, HamiltonJacobi reachability: Some recent theoretical advances and applications in unmanned airspace management, Annual Review of Control, Robotics, and Autonomous Systems, 1 (2018), 333358.
doi: 10.1146/annurevcontrol060117104941.

[15]

W. L. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Mathematische Annalen, 117 (1939), 98105.
doi: 10.1007/BF01450011.

[16]

M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.

[17]

M. Gromov, CarnotCarathéodory spaces seen from within, SubRiemannian Geometry, Prog. Math.(eds, A. Bellaiche and JJ. Risler), Birkhäuser, Basel, 144 (1996), 79–323.

[18]

M. Gromov, Metric Structures for Riemannian and NonRiemannian Spaces, Based on Structures Metriques des Varietes Riemanniennes (eds. J. LaFontaine and P. Pansu), 1981, English Translation by Sean M. Bates, Birkhäuser, Boston.

[19]

R. Hermann, Differential Geometry and the Calculus of Variations, Series: Mathematics in Science and Engineering, 49, Academic Press, New York, 1968.

[20]

C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78 (1997), 2690.

[21]

V. Jurdjevic, Geometric Control Theory, Cambridge University Press, Cambridge, UK, 1997.

[22]

D. Liberzon, Calculus of Variations and Optimal Control Theory, Princeton University Press, Princeton and Oxford, 2012.

[23]

J. Liphardt, S. Dumont, S. B. Smith, I. Tinoco Jr and C. Bustamante, Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality, Science, 296 (2002), 18321835.
doi: 10.1126/science.1071152.

[24]

I. Mitchell, The flexible, extensible and efficient toolbox of level set methods, Journal of Scientific Computing, 35 (2008), 300329.
doi: 10.1007/s1091500791744.

[25]

R. Montgomery, Review of M. Gromov, CarnotCarathéodory Spaces Seen from Within, Mathematical Reviews, 53C17 (53C23) featured review, 2000, MathSciNet, American Mathematical Society.

[26]

R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications, American Mathematical Society, Providence, RI., 2002.

[27]

K. C. Neuman and S. M. Block, Optical trapping, Review of Scientific Instruments, 75 (2004), 2787.
doi: 10.1063/1.1785844.

[28]

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, SpringerVerlag, New York, 2003.
doi: 10.1007/b98879.

[29]

S. Osher, A level set formulation for the solution of the Dirichlet problem for HamiltonJacobi equations, SIAM Journal of Mathematical Analysis, 24 (1993), 11451152.
doi: 10.1137/0524066.

[30]

B. Øksendal, Stochastic Differential Equations, Fifth edition. Universitext. SpringerVerlag, Berlin, 1998.
doi: 10.1007/9783662036204.

[31]

R. K. Pathria and P. D. Beale, Statistical Mechanics, 3$^{rd}$ edition, Elsevier, Burlington MA, 2011.

[32]

P. K. Rashevskii, About connecting two points of complete nonholonomic space by admissible curve (in Russian), Uch. Zapiski Ped. Inst. Libknexta, 2 (1938), 8394.

[33]

D. A. Sivak and G. E. Crooks, Thermodynamic metric and optimal paths, Physical Review Letters, 108 (2012), 190602.
doi: 10.1103/PhysRevLett.108.190602.

[34]

J. C. Willems, Dissipative dynamical systems part Ⅰ: General theory, Archive for Rational Mechanics and Analysis, 45 (1972), 321351.
doi: 10.1007/BF00276493.

[35]

P. R. Zulkowski, The Geometry of Thermodynamic Control, Ph.D thesis, University of California, Berkeley, 2014.

[36]

P. R. Zulkowski, D. A. Sivak, G. E. Crooks and M. R. DeWeese, Geometry of thermodynamic control, Physical Review E, 86 (2012), 041148.
doi: 10.1103/PhysRevE.86.041148.

[37]

R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford University Press, New York, 2001.
