Entropy| Entropy |
In General
> s.a. chaos; MaxEnt (Maximum Entropy Principle);
history of physics; statistical mechanics;
thermodynamics.
* Thermodynamic entropy:
An extensive thermodynamical function of state which is non-decreasing for
adiabatic transformations (constant in reversible ones); In most systems,
it grows monotonically with E; The concept was introduced by
Clausius in the 1860s and the Clausius entropy is defined, up to an
additive constant, by the relation dS = dQ/T.
* Statistical interpretation:
A measure of how spread out a classical distribution function or quantum density
ρ matrix is; For a system that can be in Ω equiprobable states
the Boltzmann entropy is SB =
kB ln Ω; More generally, for
a classical probability distribution the Gibbs entropy is SG
= −kB ∑i
pi ln pi,
and for a quantum density matrix the von Neumann entropy is S
= −kB tr ρ ln ρ;
> s.a. types of entropies.
* And classical / quantum mechanics:
In classical mechanics one assumes entropies are finite, but if one takes the
\(\hbar\) → 0 limit of any quantum entropy expression, this diverges; So
classical thermodynamics is not the classical limit of quantum statistical
mechanics, it knows about quantum mechanics.
@ Articles, II: Han et al cm/97,
AJP(99)jan [tracing over degrees of freedom];
Styer AJP(00)dec [examples and meaning];
Lieb & Yngvason PT(00)apr [without thermodynamics];
Styer AJP(08)oct [and evolution];
Salagaram & Chetty AJP(11)nov [computation].
@ Books: Martin & England 81;
Denbigh & Denbigh 85;
Leff & Rex ed-90;
Dugdale 96 [II];
Scully & Scully 07
[Maxwell's demon, information, and the quantum];
Grandy 08 [and probability];
Ben-Naim 16 [I].
@ General references:
Wehrl RMP(78);
in Sorkin PRL(86);
Mackey RMP(89) [increasing entropy and ergodicity];
Lavenda et al NCB(95);
Leff AJP(96)oct [and energy sharing];
Levy math/06 [mathematical interpretation];
Kozlov & Treshchev TMP(07) [coarse-grained];
Bernstein a1109 [pedagogical];
Baumgartner FP(14)-a1206 [axiomatic characterization and derived facts];
Zanchini & Beretta Ent(14)-a1403 [general definition];
Phillips TPT(16) [entropy as the spread of energy];
Jakšić a1806 [and information theory];
Kycia a1908 [formal overview].
@ Conceptual: Leff FP(07) [language and interpretation];
Topsoe a0807 [entropy and truth vs belief];
Timberlake TPT(10) [statistical interpretation];
Swendsen AJP(11)apr [definitions and meaning];
Baez et al Ent(11)-a1106 [characterization in terms of information loss];
Davey PhSc(11) [and probability];
Swendsen FP(12) [argument for probabilistic definition];
Dieks a1209-in [thermodynamical vs statistical-mechanical definitions];
Benguigui EJP(13)-a1209 [different definitions];
Caticha M&M-a1412
[entropic inference as a general framework for reasoning under conditions of uncertainty];
in Oltean et al PRD(16)-a1607 [nature of S];
Toffoli Ent(16)-a1705 [and "honest entropy"];
Styer TPT(19)sep [entropy isn't always disorder];
Weaver a2004 [Boltzmann and Clausius entropy];
Brandsen et al a2103 [perspective from games of chance].
@ And observation: Steane NJP(16)-a1510
[determining absolute entropy without quantum theory or the third law].
Related Concepts and Generalizations
> s.a. Coarse Graining; Disentropy;
dissipation; Entropic Dynamics;
Homogeneity.
@ And area law:
Mäkelä gq/06-GRF;
Masanes PRA(09)-a0907 [for low-energy states].
@ Other properties: Kay & Kay JPA(01)mp/98 [strong subadditivity and volume];
Touchette AJP(08)jan [(non)-concavity].
@ Subsystems: Hotta & Joichi PLA(99)cm [additivity];
Baumgartner JPA(02)mp/01;
Dupuis et al a1607 [additivity, "accumulation"].
@ Entropy current: Bhattacharyya JHEP(14)-a1403,
JHEP(14) [and the equilibrium partition function];
Banerjee et al JHEP(14) [non-relativistic fluid].
@ Beyond equilibrium situations: Beretta & Zanchini in(11)-a1010;
Beretta & Zanchini a1411,
AAPP(19)-a1911 [and few-particle systems];
> s.a. non-equilibrium thermodynamics.
@ And time: Hotke-Page & Page in(92) [clock time];
Ben-Naim 16 [no relationship].
@ Entropy production and arrow of time:
Parrondo et al NJP(09);
Martyushev & Shaiapin Ent(16)-a1605;
Mintchev & Sorba a2003-proc.
@ Related topics: Hall PRA(99)qp/98 [geometric, ensemble volume];
Leff AJP(99)dec [dimensionless];
Dover PhyA(04) [and scaling laws];
Hanel et al PNAS(12)-a1211 [generalized, for systems violating the Shannon-Khinchin axioms];
Lieb & Yngvason PRS(14)-a1403 [entropy meters and the entropy of non-extensive systems];
Plastino et al PhyA(14)
[partition function and entropy from thermodynamics];
Chafaï AFST(15)-a1405 [aspects of entropy in different disciplines].
Related topics:
see entropy bounds; entropy in quantum theory;
types of entropies and entanglement entropy.
Systems
> Gravity-related:
see black-hole entropy; gravitational
thermodynamics; horizons.
> Other systems:
see casimir effect [negative entropies];
cell complex; cellular
automaton; networks; thermodynamic
systems; tilings.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 25 mar 2021