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 d*S* = d*Q*/*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 *S*_{B} =
*k*_{B} ln Ω; More generally, for
a classical probability distribution the Gibbs entropy is *S*_{G}
= −*k*_{B }∑_{i}
*p _{i}* ln

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**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.

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