doubtless these appallingly bad physics and maths threads will continue. — Banno
The principle of causal closure is about what counts as physical. Anything that has a physical effect counts as a physical thing. We observe physical effects (galaxies rotating faster than we would otherwise expect should be possible without flying apart, and galaxies accelerating away from each other faster that we would otherwise expect), and we don't yet know what is causing them, so we give whatever those things are placeholder names, "dark matter" and "dark energy". But since they have physical effects, whatever those things turn out to be count as physical things. — Pfhorrest
Anyway, how did we get stuck on this topic of dark matter...? — Pfhorrest
Current physics do describe "dark matter" and "dark energy". These names describe physical phenomena that have been observed. — Echarmion
The entire infinite space with infinite matter, the whole system is a closed system.
— god must be atheist
Well we don't really know that, do we? — Echarmion
They are an embarrassment, really. Any curious scientist who passes by the forums would quickly and quietly move on. — Banno
Re-read my comment. There are no 'events' and there is no 'physicality' except with respect to the evolving perceptual needs of humans who consensually segment and re-segment what they call 'the world'. Ultimately all definition becomes subject to an infinite regress in which axioms like 'entropy' have ephemeral utility. Such is the basis of pragmatism versus naive realism. — fresco
And perhaps beyond those users, who by default value style over content. — god must be atheist
Entropy is a concept that is useful on a microscopic scale, but has trouble applying itself to the macroscopic one. As such, there is no such thing as "the entropy of the world, or of the universe", or even heat death of the universe owing to entropy. Entropy is even problematic in the microcosm, as studies show. — Pussycat
Max Planck wrote that the phrase "entropy of the universe" has no meaning because it admits of no accurate definition. More recently, Walter Grandy writes: "It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence." According to Tisza: "If an isolated system is not in equilibrium, we cannot associate an entropy with it." Buchdahl writes of "the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system". According to Gallavotti: "... there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state." Discussing the question of entropy for non-equilibrium states in general, Lieb and Yngvason express their opinion as follows: "Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way." In Landsberg's opinion: "The third misconception is that thermodynamics, and in particular, the concept of entropy, can without further enquiry be applied to the whole universe. ... These questions have a certain fascination, but the answers are speculations, and lie beyond the scope of this book."
A recent analysis of entropy states, "The entropy of a general gravitational field is still not known", and, "gravitational entropy is difficult to quantify". The analysis considers several possible assumptions that would be needed for estimates and suggests that the observable universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor. Lee Smolin goes further: "It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. ... Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems."
Another fundamental and very important difference is the difficulty or impossibility, in general, in defining entropy at an instant of time in macroscopic terms for systems not in thermodynamic equilibrium; it can be done, to useful approximation, only in carefully chosen special cases, namely those that are throughout in local thermodynamic equilibrium.
Max Planck wrote that the phrase "entropy of the universe" has no meaning because it admits of no accurate definition. More recently, Walter Grandy writes: "It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence1This is an assumption they can't substantiate.." According to Tisza: "If an isolated system is not in equilibrium, we cannot associate an entropy with it."2. Assumes the entire universe is not an isolated system. Buchdahl writes of "the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system". According to Gallavotti: "... there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state." Discussing the question of entropy for non-equilibrium states in general, Lieb and Yngvason express their opinion as follows:"Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way."3. READ THE WORDS: DESPITE THAT FACT THAT MOST PHYSICISTS BELEIVE IN SUCH A NON-EQUILIBRIUM THEORY In Landsberg's opinion: "The third misconception is that thermodynamics, and in particular, the concept of entropy, can without further enquiry be applied to the whole universe. ... These questions have a certain fascination, but the answers are speculations, and lie beyond the scope of this book."4. MY OPINION IS NOT, REPEAT, NOT LANDSBERG'S BOOK.
A recent analysis of entropy states, "The entropy of a general gravitational field is still not known", and, "gravitational entropy is difficult to quantify". 5. i AM NOT TALKING GRAVITATIONAL ENTROPY. The analysis considers several possible assumptions that would be needed for estimates and suggests that the observable universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor. Lee Smolin goes further: "It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. ... Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems."6 THIS HAS PATENTLY NOTHING TO DO WITH THE POINT. — Pussycat
Another fundamental and very important difference is the difficulty or impossibility, in general, in defining entropy at an instant of time in macroscopic terms for systems not in thermodynamic equilibrium; it can be done, to useful approximation, only in carefully chosen special cases, namely those that are throughout in local thermodynamic equilibrium.7 READ: AT AN INSTANT OF TIME. OUTSIDE OF AN INSTANT OF TIME IT IS NOT DIFFICULT, IT IS NOT IMPOSSIBLE. — Pussycat
My contribution here is to refer to "Poincare recurrence." Easy enough to google. Very broad strokes: the idea is that in any system, wait long enough and some configuration of it will recur — tim wood
This is a result that requires a function that takes points in the space under consideration back into that space. — jgill
My understanding was akin to shuffling a deck of cards a lot of times. — tim wood
1. All the particles in the system are bound to a finite volume.
2. The system has a finite number of possible states. — jgill
If matter has existed from infinite past, then entropy is such that it can be reset to a previous state.
If this was not true, the world would be approaching much closer to a fully entropic state than what we experience right now. Or else perhaps we'd be in a fully entropic state. — god must be atheist
Besides being an introductory text, our objective is to present an overview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description. This is partially a terra incognita, an unknown land, because basic concepts as temperature, entropy, and the validity of the second law become problematic beyond the local equilibrium hypothesis. The answers provided up to now must be considered as partial and provisional, but are nevertheless worth to be examined.
An important question is whether a precise definition can be attached to the notion of entropy when the system is driven far from equilibrium. In equilibrium thermodynamics, entropy is a well-defined function of state only in equilibrium states or during reversible processes. However, thanks to the local equilibrium hypothesis, entropy remains a valuable state function even in non-equilibrium situations. The problem of the definition of entropy and corollary of intensive variables as temperature will be raised as soon as the local equilibrium hypothesis is given up.
By material body (or system) is meant a continuum medium of total mass m and volume V bounded by a surface Σ. Consider an arbitrary body, outside equilibrium, whose total entropy at time t is S. The rate of variation of this extensive quantity may be written as the sum of the rate of exchange with the exterior d^{e}S/dt and the rate of internal production, d^{i}S/dt:
dS/dt = d^{e}S/dt + d^{i}S/dt (2.7)
Once entropy is defined, it is necessary to formulate the second law, i.e. to specify which kinds of behaviours are admissible in terms of the entropy behaviour. The classical formulation of the second law due to Clausius states that, in isolated systems, the possible processes are those in which the entropy of the final equilibrium state is higher or equal (but not lower) than the entropy of the initial equilibrium state. In the classical theory of irreversible processes, one introduces an even stronger restriction by requiring that the entropy of an isolated system must increase everywhere and at any time, i.e. dS/dt ≥ 0. In non-isolated systems, the second law will take the more general form
d^{i}S/dt > 0 (for irreversible processes) (2.10a)
d^{i}S/dt = 0 (for reversible processes or at equilibrium) (2.10b)
It is important to realize that inequality (2.10a) does nor prevent that open or closed systems driven out of equilibrium may be characterized by dS/dt < 0; this occurs for processes for which d^{e}S/dt < 0 and larger in absolute value than d^{i}S/dt. Several examples are discussed in Chap. 6.
According to it, the local and instantaneous relations between thermodynamic quantities in a system out of equilibrium are the same as for a uniform system in equilibrium. To be more explicit, consider a system split mentally in a series of cells, which are sufficiently large for microscopic fluctuations to be negligible but sufficiently small so that equilibrium is realized to a good approximation in each individual cell. The size of such cells has been a subject of debate, on which a good analysis can be found in Kreuzer (1981) and Hafskjold and Kjelstrup (1995). The local equilibrium hypothesis states that at a given instant of time, equilibrium is achieved in each individual cell or, using the vocabulary of continuum physics, at each material point.
...As a consequence, when working at short timescales or high frequencies, and correspondingly at short length scales or short wavelengths, the generalized transport laws must include memory and non-local effects. The analysis of these generalized transport laws is one of the main topics in modern non-equilibrium thermodynamics, statistical mechanics, and engineering. Such transport laws are generally not compatible with the local equilibrium hypothesis and a more general thermodynamic framework must be looked for. — chapter 7
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