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Mieli dalyviai! Visa mano kūryba ir kartu visi šie puslapiai yra visuomenės turtas, kuriuo visi kviečiami laisvai naudotis, dalintis, visaip perkurti. - Andrius




  • Irreversibility.
  • Dalis terminės energijos sistemoje, kuria negalima dirbti darbą.
  • Kaip lygiai energija yra išdalinta sistemoje.
  • Valingumas (deliberateness).

Pokalbis su Thomas Gajdosik: Thinking entropy on the quantum level. Entanglement etnropy. What is observed thermodynamical entropy. Statistical property.

Entropija - informacija yra ko reikėtų atstatyti būklę, perkeisti koordinates. Entropija + informacija = konservacija ?

Ar tyrimas yra entropijos raiška? Pavyzdžiui, metu kamuolį ant kalno viršūnės ir žiūriu, kaip jisai nuriedės, tada vėl numetu ir taip toliau. Kokia tikimybė, kad tai vyktų atbulai, atvirkščia laiko kryptimi? Tyrime laikas teka viena kryptimi, atvirkščiai tiesiog neįmanoma.

Viskas turi tą pačią temperatūrą - tai žemiausia entropija. Bet jeigu sumažiname mąstą tada temperatūros sąvoka pasikeičia.

Vietinė savybė: energijos visuma nesikeičia, tik raiška keičiasi.

Visuminė savybė: entropija didėja, energija sistemoje išsilygina.

Visuminius ir vietinius reiškinius jungia koordinačių sistema.

Teisingumas: Esame visi paskiri, nepriklausomi, kovojame už save, nevieningi. Malonė: esame visi vieningi, vienas kitą palaikome.

Penrose book

  • Walks on trees. Tree graphs - classical theory. Penrose pg.675.
  • Space time quantum unfolding. Requires self reflection?
  • If we run an experiment then... chosen by "experimenter" God... coarse graining as in entropy
  • Entropy increase <=> balanced by expansion of universe's fine scaleness
  • Low entropy = high distinction, differentiation with environment - basis for life.

Susipažinti su:


  • What is learnable?
  • What is discernible and what is not?
  • Levels like computability, complexity. A classification of dynamical systems.
  • Energy and entropy should never have been in the same units.
  • Coin toss experiment.
  • Masses far apart - you can change very little energy.
  • A little bit of energy can make a big difference. How much can you change the long term state? Control theory.
  • Certain systems are impenetrable under any algorithm that's truly random.
  • Two systems act entropically when put together lead to entropic state, bad or good, but otherwise systems for which there is no pair (love and life).
  • Energy is conserved.
  • Entropy is not fundamental. It is a convenient dynamical assumption. A shortcut principle for predicting the final state. Whether a certain arrangement of mass..
  • Entropy Demystified

Virsmo taškas: kaip maži dalykai daro didelę įtaka - žemos entropijos esmė - valdymo teorijos esmė.

Entropy and local structure

I've been reading through parts of "The Road to Reality" by John Penrose. (Here is a free download).

It's 1,000+ pages. I wish I had gotten to read it in grad school. It's a very explanatory survey of the mathematical ideas behind all of physics. I'm jumping around, reading the end, the beginning, and chapters in the middle. He provides a lot of intuition so that on a first read I don't have to worry about understanding all of the details. So it's very inspiring to feel that I have a chance to grapple with the big picture and learn about different mathematical structures and why it might be worthwhile to study them.

I've come anew to this subject because of my interest in entropy. I've been trying to summarize my philosophy, especially the different ways of looking at things from God's point of view. The concept of entropy distinguishes the bad kid's point of view (that we live in "justice", a closed system that is zero-sum and can only get worse) and the good kid's point of view (that we live in "grace", an open system that is fed by an external source of love). There is a key ambiguity between these two points of view: Is our system open or closed?

Taking up Penrose's book, I've gotten interested in physics more generally, trying to get an inkling of quantum field theory. Overall, it's interesting that the idea of entropy seems to be quite central to the big picture. I have very much to learn and relearn.

Penrose's book has quite a lot to say intuitively about entropy. For example, he notes that, counterintuitively, as regards gravitational force, entropy is lower when matter is spread out in space, and entropy is higher as matter comes together in a small area. He is also critical of the kind of open/closed system distinction that I made as regards an external energy source. He notes that the earth reflects the same amount of energy as it receives from the sun. The key point is that the energy coming in from the sun is qualitatively different. It is fewer photons of higher energy. The reflected photons are greater in number and lower in energy. The entropy is lower when there are fewer photons.

The main idea that comes to me is that there should be a very conceptual accord between the global, external geometry of the universe (an ever expanding "big bang") and the local, internal geometry of the universe (an ever refining grid as per an ever shrinking Plank's constant). Conceptually, they should be inverses of each other. This would address many issues:

  • The universe unfolds in complexity, manifests as space-time both expanding globally and refining locally, with both of equal importance.
  • The universe evolves not from an infinitesimal point but rather from a mid-scale unity of the lowest possible entropy (=1). Which is to say, the universe is most deliberate.
  • The universe manifests a clear teleology towards a 3-dimensional Euclidean space. Globally it tends towards infinite height, width, length and locally it tends towards a real number continuum. This is why classical physics works. It is based on the ultimate ideal towards which the universe is tending.
  • Whereas the universe that we actually experience is but a finite model that is tending towards the ideal. Locally it is limited by Plank's constant, the Heisenberg uncertainty principle, which however becomes ever more refined as the universe unfolds.
  • The act of measurement is what drives the unfolding of the universe. This is an act that needs to be defined. But basically it is an intervention which indicates that a particular possibility manifested among a variety. It really should be thought in terms of a refinement of the local grid of uncertainty. It's not so much that certainty was created but that uncertainty was given structure. Entropy can thus be defined not in terms of particles and their states but rather in terms of the quanta of uncertainty which keep increasing as the grid grows more refined locally.
  • Measurement also shifts from the complex valued "current model" to the real valued teleological "ideal".
  • We thus live in a world where there is a lot of instability, logically.
  • A lot of quantum structures are internal to particles and as such do not participate in the unfolding real space. For example, as Penrose describes based on twistors, the electron consists of a zig and zag, both moving at the speed of light but in opposite direction, coupled by the mass of the electron. Quantum interactions would be rethought in terms of how they give shape to "the edge" of the universe locally and globally.
  • The major error in current theories is that they presume an infinite number of states. This is a confusion and conflation of the current-finite-complex state and the ultimate-infinite-real state. The correct theory would have simply a finite series of states of possibly unknown length. The current theories thus yield infinite nonsense which has to be worked around through renormalization.
  • Built into the notion of entropy is the idea of a coarse grid, and I imagine, a hierarchy of several grids (perhaps three or four) of increasing refinement. So these grids would have explicit physical meaning.
  • The difference between gravitational and quantum perspectives would be fundamental and related to the different ways that they exhibit entropy, where gravity is low entropy when it is spread out, and quantum behavior is vice versa.
  • There would be pairing of global and local phenomenon. For example, an electron would pair with a white-dwarf (composed of electron-degenrate matter), a neutron with a neutron star, and so on. Which is to say, both phenomemon would be considered equally fundamental. A neutron locally has the same complexity, conceptually as a neutron star globally. They are at opposite ends of the spectrum and remain so as the universe unfolds.

So these are some of the kinds of ways that physics could be thought of as describing the unfolding of "the edge" of the universe, which happens both locally and globally.

I was surprised to hear that there might not have been much thinking along such lines because it seems to suggest itself.

Entropy and coincidence

I have a bucket of ash in my room which I accidentally knocked over. So that created a mess.

That helped me realize what it means that from the point of view of the law of physics, it would be possible for all of the interactions to be reversed so that the ash climbed back into the bucket. It means that there is heat energy - kinetic energy of particles - such that if the momentum was all reversed, then those particles would all coincidentally work together and impart their energy to push all of those specks of ash and knock the bucket vertical with all the ash inside, and knock my foot, too. Such a coincidence is possible but it would be amazing.

It seems the main point is that when we have an interaction, the outputs can exceed the inputs. In which case it would require an enormous amount of coincidence to reverse it. So entropy is the measure of that coincidence.

And coincidence is a concept that brings together time and space, although I have yet to understand it. Coincidence has to do with the relationship between subsystems and systems. In physical modeling it's crucial that we be able to talk about subsystems. But how do those subsystems come back together?


Naujausi pakeitimai

Puslapis paskutinį kartą pakeistas 2016 gruodžio 01 d., 21:52