@Danu Not really, it is evidently incompatible with entropy in terms of probabilities, i.e. $\sum_i p_i\ln(p_i)$ or $\int p \ln(p)$ since the $p_i$ there are fractions.
@Danu I don't recognize thermodynamics as distinct from statistical mechanics. All thermodynamics is is equilibrium statistical mechanics disguising itself by using strange historical approaches :P
@Danu I'm not following you. What do you think is the difference between equilibrium statistical mechanics for large particle numbers and thermodynamics?
It's as rigorous as the "continuum limit", I think. That is, in many cases you can take it, and it is provable it exists, but there might be annoying cases where the limit doesn't (naively) exist
user54412
Just to spur on discussion, can't we have thermodynamics of systems not composed of Newtonian billiard balls?
One professor once noted to me that it's a shame people only learn stat mech and not traditional thermo, since practically there exist systems where we don't have a description in terms of large numbers of particles, but we do have empirically valid notions of temperature and so on.
(taken a course on everything; I already did the AdS/CFT course!)
In other news, my algebraic topology TA laughed in my face when he heard I was interested in taking the upcoming course on group cohomology. He said "maybe I will take that course" (he's a postdoc)
@Danu We did a little bit of thermo in an experimental lecture that was already crammed with mechanics and electrodynamics, but I mainly had stat mech. That might have shaped my view :P
@Danu I'm not sure whether they are trying to select for people who enjoy those boring computations or whether they genuinely think they are presenting their field in an attractive manner
I am certainly no fan of computing Feynman diagrams, but I think you need to see at least a derivation of the LSZ formula and some explicit computations in QED to really understand how QFT works and how it gets its predictions. And it doesn't hurt to do perturbative renormalization so you get an appreciation for the people who actually calculate stuff
@Danu What did you do to calculate it? Triangle diagrams? Fujikawa method? Just abstract A-S application?
If something is really awkward to express coordinate-free, then don't do it. But I think e.g. electrodynamics and QFT would be a lot more beautiful if they didn't write everything in indices
@0celo7 Ah, well, there we disagree. I definitely prefer the latter notation because it makes the relation between the objects more clear - it is H that eats u, and still can eat another vector. I just don't see that in the first version
@BernardMeurer A continuous deformation; a space locally modelled on $\mathbb{R}^n$; any differentiable function but a few ones; "on it" = function from it to the reals.
@BernardMeurer That's fine, but you won't learn stuff if I just explain words you don't know with words you don't know, and I won't improvise an intro to topology and analysis right now
Uh, I am not making a joke or anything. The thing is, I am kinda aware there are many economic models. Recently in a talk I learnt about a model called steady state economics. I am just wondering how it compares with other models like what are the pros and cons on using them?
The response just a few lines above is the reason why before realising economics has a non human factor, I often refrain from asking economics questions, because people tend to start thinking about money and corruption, and then turned the question into a joke
Economic growth is frequently expressed as a % of GDP. Proponents of a steady-state economy postulate that perpetual exponential economic growth is impossible and that any system relying on it is inherently unstable. Is this true?
Is indefinite exponential economic growth possible?
(See also: ...
One of the most widely published measures of the economy is the economic growth as a % of the GDP; i.e. the degree to which an economy grows exponentially. In my understanding, when the rate of economic growth is declining or close to 0%, this is considered undesirable and acts are undertaken to...
I'm puzzled by the core example of an economy populated by firms with a constant returns to scale production function operating under perfect competition, where no income remains after paying out competitive wages to workers (L) and competitive return to the capital hired for production (K). Mean...
QUESTION: What are the major or systematic applications of post-1960s mathematics to microeconomics?
For example, in the late 19th century, Fisher first used the mathematical ideas of Gibbs to construct modern utility theory. In the 20th century, Mas-Colell incorporated topological ideas to...
Ecological economics/eco-economics refers to both a transdisciplinary and interdisciplinary field of academic research that aims to address the interdependence and coevolution of human economies and natural ecosystems over time and space. It is distinguished from environmental economics, which is the mainstream economic analysis of the environment, by its treatment of the economy as a subsystem of the ecosystem and its emphasis upon preserving natural capital. One survey of German economists found that ecological and environmental economics are different schools of economic thought, with ecological...
I recall being stunned (they can do that?) by the mere mention of the technique called "Zeta Function Regularization", see http://en.wikipedia.org/wiki/Renormalization, http://en.wikipedia.org/wiki/Zeta_function_regularization ,
to sum divergent series like zeta(-n) to get finite results.
I tho...
Nice to see that mathematicians are finally spending their time wisely. Now if only those pesky algebraic geometers and number theorists got their shit together...