Category Theory
Zulip Server
Archive

You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.

Stream: deprecated: thermodynamics

Topic: the right word for the job

Owen Lynch (Feb 19 2022 at 17:32):

Isenergic is a misnomer, because we are really talking about power, not energy. Luckily, there's a word for "equal power" already: isocratic! Thus, I propose the coining "isocratic subspace" and "isocratic relation", as analogues of "Lagrangian subspace" and "Lagrangian relation."

Owen Lynch (Feb 19 2022 at 17:37):

Maybe a vector space with a (n,n) bilinear form (i.e., $V \times V^\ast$) can be called a "cratic vector space"

Owen Lynch (Feb 19 2022 at 17:37):

The root "crat" is greek for "power"

Owen Lynch (Feb 19 2022 at 17:39):

Another option would be "http://www.perseus.tufts.edu/hopper/morph?l=i%29soduname%2Fw&la=greek&can=i%29soduname%2Fw0&prior=fwtobi/as"--isodunamous

Owen Lynch (Feb 19 2022 at 17:43):

Eh

Owen Lynch (Feb 19 2022 at 17:44):

I think I like isocratic

Matteo Capucci (he/him) (Feb 19 2022 at 18:03):

Mmh 'kratos' is quite a different meaning of 'power', as it means somehting like 'dominance'. 'Energeia' means 'power' in a dynamic sense (indeed, there's also 'dinamis'). So 'isocratic' would be a misnomer, while 'isoenergonic'/'isonergetic' might actually be closer.

Matteo Capucci (he/him) (Feb 19 2022 at 18:06):

You could try 'sthenos' which means 'power, might' (in a violent sense though) and go with 'isosthenic', though I don't recall it being used like this in science.
Alternatively you could go with Latin and have 'isopotent'.

Owen Lynch (Feb 19 2022 at 18:23):

Hmm, I guess the problem is that people often use "power" to mean "the ability to do work", i.e. "By the power of greyskull", etc.

Owen Lynch (Feb 19 2022 at 18:23):

Which is something different than "instantaneous work supplied"

John Baez (Feb 20 2022 at 00:44):

Are you making up a new name for 'Dirac structure' - if so, don't: that's just a way to get people to not read your thesis - or are you making up a new name for a new concept?

Owen Lynch (Feb 20 2022 at 01:18):

Yeah, I think you're right... The thing that's missing is a name for the relation; it's kind of clunky to say "Dirac structure on the product"

Owen Lynch (Feb 20 2022 at 01:18):

Maybe I could coin "Dirac relation"?

John Baez (Feb 20 2022 at 02:15):

Dirac relation sounds great to me! People talk about Lagrangian relations, etc.

John Baez (Feb 20 2022 at 02:15):

I don't think "Diracian" is good. :upside_down:

John Baez (Feb 20 2022 at 02:16):

Can you cook up a symmetric monoidal category of (some sort of???) manifolds and Dirac relations?

Owen Lynch (Feb 20 2022 at 03:21):

A Dirac relation isn't between two manifolds... I don't think

Owen Lynch (Feb 20 2022 at 03:21):

It would be between two... Courant algebroids?

Owen Lynch (Feb 20 2022 at 03:22):

In the non-differential geometry setting, it's just between two vector spaces that have (n,n) forms on them

John Baez (Feb 20 2022 at 03:24):

Hmm. I'm a bit confused know. Are you using a Dirac manifold to be a 'phase space' and a Dirac relation to be a relation between phase spaces?

Owen Lynch (Feb 20 2022 at 04:07):

What is a Dirac manifold?

John Baez (Feb 20 2022 at 05:00):

A [[Dirac manifold]] is a manifold with a Dirac structure. This generalizes the concepts of Poisson manifold and presymplectic manifold, so a Dirac manifold is a general concept of 'phase space'.

Owen Lynch (Feb 20 2022 at 14:55):

Ah! The trouble is, the manifold in a port-Hamiltonian system does not necessary have a Dirac structure in that sense

Owen Lynch (Feb 20 2022 at 14:55):

Rather, there is a Dirac structure on $T_x X \times T^\ast _x X \times \mathcal{E} \times \mathcal{F}$

Owen Lynch (Feb 20 2022 at 14:56):

Where $\mathcal{E}$ and $\mathcal{F}$ are spaces of efforts and flows, respectively

Owen Lynch (Feb 20 2022 at 14:57):

So the objects of this SMC should be Courant algebroids, and then a morphism is a Dirac structure on the product of two Courant algebroids

Owen Lynch (Feb 20 2022 at 14:59):

The nLab redirects Lie 2-algebroid to Lie infinity-algebroid...

Owen Lynch (Feb 20 2022 at 14:59):

Is there a less homotopic definition?

John Baez (Feb 20 2022 at 15:16):

Probably someone has written down the definition of a Lie 2-algebroid without use of infinity-stuff, but I don't know where. As you (now) know, Alissa Crans and I wrote down the definition of Lie 2-algebra in various ways, and blending these with the definition of [[Lie algebroid]] should give various equivalent definitions of Lie 2-algebroid.