Thermodynamics

In General > s.a. history; information; Kinetic Theory; quantum field theory; statistical mechanics; concepts and systems.
* Idea: It studies the relationship between heat and work; Uses macroscopic variables as the basic ones, n or N, p, V, T, chemical potential , related by an equation of state.
* Motivation: Originally, it was important because of engineering applications (heat work in locomotives; Work heat in cannon boring and Joule's experiments; Now it is important because it involves the relationship between macroscopic and microscopic descriptions, information, and time.

Zeroth Law
* Idea: Two thermodynamical systems which are both in equilibrium with a third one are also in equilibrium with each other.
@ References: Ramírez-Hernández et al PRL(08) [violation, with negative specific heat].

First Law > s.a. heat [including engines].
* Idea: The change in the internal energy of a system, from heat dQ absorbed and work dW done, dU = dQ – dW.
* Heat absorbed: The term dQ can be written as mc(T) dT, where m is the mass and c the specific heat (at constant volume), or TdS, depending on which variables are used.
* Work done: The term dW can have contributions from different processes, for example dW = p dV + t dA + f dL – dN + dQ + (see black hole laws) + ...; Here, p is the pressure, t surface tension, f tension, chemical potential.
* Remark: dU is a sum of products of conjugate quantities, Intensive · d(Extensive).
@ References: Kapoulitsas PS(03) [new formulation]; Martinez et al PhyA(05), Plastino et al PhyA(06) [from information theory].

Second Law > s.a. energy conditions [violations]; entropy; H Theorem; Maxwell's Demon; systems.
$ Kelvin: Not all heat can be converted into work with no other change in the system or surroundings.
$ Clausius: No cyclic engine can just transfer thermal energy from a colder body to a hotter one.
$ Minimal work principle: One of the formulations of the second law, states that work done on a thermally isolated equilibrium system is minimal for adiabatically slow (reversible) realization of a given process.
* Remark: It is not synonymous with inescapable collapse into disorder, but allows self-organization.
* Carnot cycle: All Carnot cycles between the same two temperatures have the same efficiency, = (Q₁–Q₂)/Q₁ = (T₁–T₂)/T₁; Any other engine between the same temperatures is less efficient.
@ General references: Marcella AJP(92) [and entropy]; Bennett SA(87)nov [demons]; Atkins 94 [I]; Berger PE(94)ao/95 [interpretation]; Allahverdyan & Nieuwenhuizen cm/04 [minimal work]; Maes & Tasaki LMP(07) [macroscopic system + microscopic degrees of freedom]; Sheehan FP(07) [foundations and status]; Lemos & Penner AJP(08) [Sadi Carnot]; Campisi SHPMP(08) [proof based on volume entropy].
@ New views, generalizations: Lieb & Yngvason PRP(99), PT(00)mp, mp/02-in; Davies & Davis FP(02)ap/03 [with black holes]; Gyftopoulos & Beretta qp/05; Zhang qp/06, Duncan & Semura FP(07) [and info theory].
@ On violations: PW(90)dec [perpetual motion]; Wang et al PRL(02) [short time, mesoscopic]; Minkel SA(03)jun [quantum]; Ford & O'Connell PRL(06)qp [quantum, and resolution]; Gytopoulos & von Spakovsky a0706, a0706, Gyftopoulos a0706 [no nanoscale violations].
@ Related topics: Berger IJTP(90) [Szilard's demon]; Uffink SHPMP(01) [and arrow of time]; Allahverdyan & Nieuwenhuizen cm/01 [basis]; Martín-Olalla & Rey de Luna JPA(03) [and Nernst theorem]; Feng EJTP(04)qp/05 [microscopic origin]; > s.a. quantum measurement.

Third Law > s.a. black hole thermodynamics; brownian motion; Free Energy.
* Idea: As T → 0, the heat capacity of a thermodynamical system goes to zero; In the Nernst formulation, in as T → 0, S → 0 or a constant, independent of all parameters of the system.
@ References: Lavenda & Gunning-Davies NCB(95); Blau & Halfpap AJP(96)Q; Dimitrov qp/97; Wald PRD(97)gq [black holes and limitations]; Belgiorno JPA(03), JPA(03); O'Connell JSP(06)qp [quantum regime]; Wreszinski & Abdalla a0710 [precise formulation and applications].

Related Topics > see Contact Geometry; hamilton-jacobi theory; Initial Conditions; modified thermodynamics [including non-equilibrium]; .

References > s.a. computation and computational physics; generalized; history; teaching; statistical mechanics.
@ Books, I: Goldstein 93; Schneider & Sagan 05 [and life]; Atkins 07.
@ Books, II: Bergmann 62; Morse 64; Berry 91; Bailyn 94 [historical]; Carrington 94; Lee 02 [entropy, free energy]; Turns 06; Blundell & Blundell 06 [r PT(07)oct]; Stowe 07.
@ Books, III: O'Connell & Haile 05 [chemical engineering]; Cheng 06 [statistical]; Honig 07.
@ Books, problems: Lim 90.
@ Books: Bridgman 41 [conceptual]; Fermi 57; Pippard 64; Schrödinger 64; Kittel & Kroemer 80; Truesdell 84; Callen 85; Griffiths 85; Guggenheim 85; Waldram 85; Martin 86; Bauman 92; Greiner et al 95; Zemansky & Dittman 97.
@ Conceptual foundations: Emch & Liu 02 [logic]; Callender SHPMP(01) [re taking thermodynamics too literally]; Hemmo & Shenker SHPMP(01), PhSc(03), SHPMP(05) [from decoherence?]; Antoniou FP(02) [Carathéodory]; Mahler et al PhyE(05)qp [in composite systems]; Abou Salem & Fröhlich mp/06/JSP [status of laws]; > s.a. statistical mechanics [equilibrium].
@ Geometric: Chen JMP(99); Quevedo JMP(07)phy/06; Quevedo & Vázquez a0812-in [geometrothermodynamics]; > s.a. black hole thermodynamics.
@ Mathematical foundations: Giles 64; Owen 84.
@ Other topics: Maslov TMP(94) [Hamiltonian and quantization]; Hannay AJP(06) [Carnot's vector field formulation].
> Online resources: Internet Encyclopedia of Science pages.

‘In this house, young lady, we OBEY the laws of thermodynamics’
Homer Simpson punishing Lisa for making a perpetual motion machine

Main page – Abbreviations – Journals – Comments – Other sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 5 jul 2008