By D.R. Owen

ISBN-10: 0387908978

ISBN-13: 9780387908977

Examine long ago thirty years at the foundations of thermodynamics has led not just to a greater figuring out of the early advancements of the topic but in addition to formulations of the 1st and moment legislation that allow either a rigorous research of the implications of those legislation and a considerable broadening of the category of platforms to which the legislation can fruitfully be utilized. in addition, modem formulations of the legislation of thermodynamics have now accomplished logically parallel kinds at a degree available to less than graduate scholars in technology and engineering who've accomplished the normal calculus series and who desire to comprehend the function which arithmetic can play in medical inquiry. My target in penning this publication is to make a few of the modem enhance ments in thermodyamics on hand to readers with the historical past and orientation simply pointed out and to provide this fabric within the type of a textual content compatible for a one-semester junior-level path. such a lot of this presentation is taken from notes that I assembled whereas educating this sort of direction on events. i discovered that, other than a quick assessment of line integrals and unique differentials in dimensions and a brief dialogue of infima and suprema of units of actual numbers, juniors (and even a few mature sophomores) had adequate mathematical historical past to deal with the subject material. a few of the scholars whom I taught had very constrained event with formal and rigorous mathematical exposition.

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H. Kim, T. W. Kim, Heat engine driven by purely quantum information. Phys. Rev. Lett. 111, 230402 (2013) 39. H. Tajima, Second law of information thermodynamics with entanglement transfer. Phys. Rev. E 88, 042143 (2013) 40. H. 3776 (2013) 41. M. Horowitz, M. Esposito, Thermodynamics with continuous information flow. Phys. Rev. X 4, 031015 (2014) 42. D. C. Barato, U. Seifert, Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell’s demon interpretation. J. Stat.

Phys. Rev. E 84, 061110 (2011) References 49 22. M. Bauer, D. Abreu, U. Seifert, Efficiency of a Brownian information machine. J. Phys. A 45, 162001 (2012) 23. T. Sagawa, M. Ueda, Nonequilibrium thermodynamics of feedback control. Phys. Rev. E 85, 021104 (2012) 24. T. L. Rosinberg, Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited. J. Stat. Mech. P05010 (2012) 25. M. Esposito, G. Schaller, Stochastic thermodynamics for Maxwell demon feedbacks.

8) Substituting Eq. 9) where xt := x(t) denotes the state at time t, and Nx is the normalization constant which satisfies d xt+dt p(xt+dt |xt ) = 1. 6) at time t + dt is defined as 28 3 Stochastic Thermodynamics for Small System p B (xt |xt+dt ) := G(xt+dt ; xt ; t + dt) = Nx exp − (γxt − γxt+dt + ∂x U (xt+dt , t + dt)dt)2 . 11) kB T x where d x = xt+dt − xt and ◦ denotes the Stratonovich integral defined as f ◦ d x(x, t) := [ f (xt+dt , t + dt) + f (xt , t)](xt+dt − xt )/2 for any function f (x, t).

### A First Course in the Mathematical Foundations of Thermodynamics by D.R. Owen

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