# Entropy Definition and 268 Discussions

Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.The thermodynamic concept was referred to by Scottish scientist and engineer Macquorn Rankine in 1850 with the names thermodynamic function and heat-potential. In 1865, German physicist Rudolph Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature. He initially described it as transformation-content, in German Verwandlungsinhalt, and later coined the term entropy from a Greek word for transformation. Referring to microscopic constitution and structure, in 1862, Clausius interpreted the concept as meaning disgregation.A consequence of entropy is that certain processes are irreversible or impossible, aside from the requirement of not violating the conservation of energy, the latter being expressed in the first law of thermodynamics. Entropy is central to the second law of thermodynamics, which states that the entropy of isolated systems left to spontaneous evolution cannot decrease with time, as they always arrive at a state of thermodynamic equilibrium, where the entropy is highest.
Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics, and found the link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behavior, in form of a simple logarithmic law, with a proportionality constant, the Boltzmann constant, that has become one of the defining universal constants for the modern International System of Units (SI).
In 1948, Bell Labs scientist Claude Shannon developed similar statistical concepts of measuring microscopic uncertainty and multiplicity to the problem of random losses of information in telecommunication signals. Upon John von Neumann's suggestion, Shannon named this entity of missing information in analogous manner to its use in statistical mechanics as entropy, and gave birth to the field of information theory. This description has been proposed as a universal definition of the concept of entropy.

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1. ### B Entropy change for reversible and irreversible processes

I came across the following statement from the book Physics for Engineering and Science (Schaum's Outline Series). I cannot seem to find a satisfactory answer to the questions. Is the statement in above screenshot talking about entropy change the statement of Second Law of Thermodynamics or is...
2. ### I Two Entropy scenarios on a system

Entropy question. Take a finite number of identical atoms in a specific volume of space at a moment of time. Run two thought experiments on this system scenarios (both time independent) 1: expand the volume of space of the system instantaneously by a factor of 10. The fixed number of atoms...
3. ### A Free expansion of an ideal gas and changes in entropy

For a freely expanding ideal gas(irreversible transformation), the change in entropy is the same as in a reversible transformation with the same initial and final states. I don't quite understand why this is true, since Clausius' theorm only has this corrolary when the two transformations are...
4. ### I Physics of paper absorbing Water -- Doesn't this decrease Entropy?

Summary: doesn't this decrease entropy ? Cellulose is known for its hydrophilic quality, which can be explained from the polarity of its hydroxyl groups. We all know water can overcome the force of gravity through a piece of paper you put in the water. Correct me if I'm wrong but this is a...
5. ### B Does gravity defy the 2nd Law?

Summary: Trying to understand the relationship between gravity, thermodynamics and entropy, thank you. Gravity can take a diffuse cloud of gas filling a given volume of space at equilibrium density and temperature, and turn it into a burning star surrounded by empty space. Does this mean that...
6. ### I Can Core Theory Be Derived From Nine Lines?

Christoph Schiller, "From maximum force to physics in 9 lines -- and implications for quantum gravity" arXiv:2208.01038 (July 31, 2022). This paper asserts that nine propositions can be used to derive the Standard Model and GR and can point the way to quantum gravity, although he cheats a bit...
7. ### I Boltzmann Entropy Formula – Derivation

Boltzmann entropy definition is given by: $$S = k_B lnW$$ where ##W## is the weight of the configuration which has the maximum number of microstates. This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...
8. ### I Would infinite entropy break all symmetries?

If the Universe could somehow reach a state of infinite entropy (or at least a state of extremely high entropy), would all fundamental symmetries of the physical laws (gauge symmetries, Lorentz symmetry, CPT symmetry, symmetries linked to conservation principles...etc) fail to hold or be...
9. ### I Problem regarding understanding entropy

I was reading about thermodynamics postulates when i came over the differnetial fundamental equation: I understand that the second element is just pressure and last element is chemical energy, but he problem is i don't understand what is the use of entropy and how does it contribute to a...
10. ### I Unified Field Theory

Is there any approach in any books out there, where we consider that in universe exists only one field, let it be called the Unified Field (UF), in which all of the known fields (gravitational, EM field, quark field, gluon field, lepton field, Higgs Field, e.t.c.) are just components (pretty...
11. ### Change of entropy in the Universe in a thermodynamic cycle

(a) We first find that: ##T_A=\frac{P_A V_A}{nR}=\frac{1\cdot 10^5 \cdot 4}{40\cdot 8.314}K\approx 1202.7904 K##, ##\frac{T_B}{T_A}=\frac{\frac{P_B V_B}{nR}}{\frac{P_A V_A}{nR}}=\frac{P_B V_B}{P_A V_A}=\frac{P_A \frac{V_A}{2}}{P_A V_A}=\frac{1}{2}##, ##\frac{T_C}{T_B}=\frac{P_C...
12. ### A Is there a generalized second law of thermodynamics?

Hi Pfs, There are different kinds of entropies. I discoved the free entropy. https://arxiv.org/pdf/math/0304341.pdf the second law says that the total entropy cannot decrease when time goes by. Is it always the same "time" for the different entropies? the author, Voiculescu, wrote articles...
13. ### A Definition of entropy for indistinguishable and distinguishable particles

I have a rather general question about the definition of entropy used in most textbooks: S = k ln Ω, where Ω is the number of available microstates. Boltzmann wrote W rather than Ω, and I believe this stood for probability (Wahrscheinlichkeit). Obviously this is not a number between 0 and 1, so...
14. ### I Thermodynamic Identity

I have a question about the Thermodynamic Identity. The Thermodynamic Identity is given by dU = TdS - PdV + \mu dN . We assume that the volume V and that the number of particles N is constant. Thus the Thermodynamic Identity becomes dU = TdS . Assume that we add heat to the system (we see that...
15. ### Enthelpy and Isentropic compression/expansion

In a certain thermodynamics textbook, specific work done by an isentropic compressor/pump in an ideal rankine cycles, is given by the following; Wpump = h2 - h1 Wpump = v(P2 - P1), where v = v1 When I carry out these two calculations between any two states, I get vastly different answers...
16. ### Entropy of spin-1/2 Paramagnetic gas

As we know, dipole can be only arranged either parallel or anti-parallel with respect to applied magnetic field ## \vec{H} ## if we are to use quantum mechanical description, then parallel magnetic dipoles will have energy ## \mu H ## and anti-parallel magnetic dipoles have energy ## -\mu H##...
17. ### I Entropy after the Big Bang

If the universe was very hot right after the Big Bang how come the entropy of the universe was lower at that point than now? Isn't heat a reason for higher entropy?
18. ### I Elementary Ideas About Entropy -- Is this textbook example correct?

Summary:: An elementary example calculation involving entropy in a textbook seems wrong I was reading an elementary introduction to entropy and the second law of thermodynamics. The book gave the example of a gas in a chamber suddenly allowed to expand into an additional portion of the...
19. ### I Entropic effects of the Uncertainty Principle?

Per the Heisenberg uncertainty principle, a particle does not have a precisely defined location. Does such uncertainty contribute to the transfer of thermal energy (i.e. entropy)? Is uncertainty the primary means for the transfer of thermal energy at the quantum level?
20. ### Coping mechanisms for thermodynamics?

Wasn’t sure whether I should post this here since it’s a more qualitative question, or under the Thermodynamics thread because that’s a more specific topic. For all practical purposes, the laws of thermodynamics are inviolable, and statistical mechanics puts them on an even firmer theoretical...
21. ### I Entropy change due to heat transfer between sources

Hi, starting for this thread Question about entropy change in a reservoir consider the spontaneous irreversible process of heat transfer from a source ##A## at temperature ##T_h## to another source ##B## at temperature ##T_c## (##T_h > T_c##). The thermodynamic 'system' is defined from sources...
22. ### I Theoretical maximum efficiency of a heat engine without Carnot

Through an intriguing fictitious dialog between Sadi Carnot and Robert Sterling, Prof. Israel Urieli of the Ohio University shows that it is not required to invoke entropy, the second law of thermodynamics, and the Carnot cycle with the [ideal] adiabatic processes in order to find out the...
23. ### Thermodynamics of chemical reactions

In chemical reactions generally ΔG < 0 , but if we were to consider a reversible path between pure reactants and products at 1 bar pressure , shouldn't the ΔG = 0 for every reaction ? and if it is due to non-pv work , I don't see any non pv work being done in reactions happing in a closed...
24. ### Protein Folding Entropy

I have been reading about protein thermodynamics and found different types and models for entropy calculation before and after protein folding. I understand Vibrational, conformational, configurational entropy are some of the most studied "types" of protein folding entropy. My questions is...
25. ### Number of moles necessary to get piston back to initial position

a) ##T_A=\frac{p_AV_A}{nR}=300.7K, P_A V_A=kL^2=nRT_A##, ##P_B S=k\frac{L}{2}\Rightarrow P_B V_B=k(\frac{L}{2})^2 \Rightarrow P_B=\frac{kL^2}{2V_A}=\frac{P_AV_A}{2V_A}=\frac{P_A}{2}##, ##W_{spring\to gas}=\int_{L}^{L/2}kxdx=-\frac{3}{8}kL^2=-\frac{3}{8}nRT_A####\Rightarrow Q=L+\Delta...
26. ### Finding the increase in entropy of the universe in gas expansion

a) ##P_f=\frac{nRT_f}{V_f}=\frac{nR\frac{T_i}{2}}{2V_0}=\frac{1}{4}\frac{nRT_i}{V_0}=\frac{1}{4}P_i## b) ##Q=\Delta U=nC_V \Delta T=n\frac{5}{2}R(-\frac{T_i}{2})=-\frac{5}{4}nRT_i=-\frac{5}{4}P_i V_0## (##L=0## since the gas expands in a vacuum; Now, (a) and (b) are both correct but not (c)...
27. ### I Defect concentration formula w/o Stirling approximation

In many cases, the concentrations of defects or charges are quite big enough to use SA, due to a big number of Avogadro's number. The derivation for the well-known formula of a defect concentration is followed. If the n_v is expected to be lower than 1, then it would be impossible to use SA...
28. ### I Why does entropy grow when a solar system is formed?

On page 50 of "From eternity to here", Sean Carroll writes that the protostellar cloud had a lower entropy than the solar system it produced. That strikes me as odd. A solar system looks more arranged than a dust cloud. When talking about entropy, someone always mentions the milk in the coffee...
29. ### B Is time a consequence of 2nd law of thermodynamics?

I have heard from a knowledgeable physics proffessor, time exists independently and it is not a consequence of arrow of time. Could some body explain this?
30. ### I Entropy and Heat Capacity Relation

I have a simple question sort of about exact differentials and deciding which variables matter and when. I know we can write entropy ##S## as ##S(P,T)## and ##S(V,T)## to derive different relations between heat capacities ##C_V## and ##C_P##. I was wondering if it is technically correct to...
31. ### Calculating work and heat transfer in this Carnot process

Hey guys! This is problem from Callens Thermodynamics textbook and I'm stuck with it. My goal was to get a expression for the entropy ##S## which is dependent on ##T## so I can move into the ##T-S##-plane to do my calculations: I startet by expressing the fundamental equation as a function of...
32. ### Bose gas versus Classical gas

In classical statistics, we derived the partition function of an ideal gas. Then using the MB statistics and the definition of the partition function, we wrote: $$S = k_BlnZ_N + \beta k_B E$$, where ##Z_N## is the N-particle partition function. Here ##Z_N=Z^N## This led to the Gibb's paradox...
33. ### Calculating specific heat capacity from entropy

Hey guys! I'm currently struggling with a specific thermodynamics problem. I'm given the entropy of a system (where ##A## is a constant with fitting physical units): $$S(U,V,N)=A(UVN)^{1/3}$$I'm asked to calculate the specific heat capacity at constant pressure ##C_p## and at constant volume...
34. ### Calculate change in entropy per minute.

So what I did was find the change in Q per min. Mass melted per min * latent heat capacity = Q per min = 11.5 kg /min * 3.4*10^5 J/kg = 3910000 J/min Now the equilibrium temperature is 100 degrees Celsius or 373.15 degrees kelvin. If I do 3910000 J/min / 373.15 K I get 10478 J/(K*min). This...
35. ### Definition of a system in Boltzmann entropy

Context Boltzmann first defined his entropy as S = k log(W). This seems to be pretty consistently taught. However, the exact definitions of S & W seem to vary slightly. Some say S is the entropy of a macrostate, while others describe it as the entropy for the system. Where the definition of...
36. ### I How can a process be isentropic but not reversible or adiobatic?

In the book for our thermodynamics, it states that a process that is internally reversible and adiabatic, has to be isentropic, but an isentropic process doesn't have to be reversible and adiabatic. I don't really understand this. I always thought isentropic and reversible mean the same thing...
37. ### Find change in entropy for a system with a series of reservoirs

I've calculated the change in the entropy of material after it comes in contact with the reservoir: $$\Delta S_1 = C \int_{T_i+t\Delta T}^{T_i+(t+1)\Delta T} \frac{dT}{T} = C \ln{\frac{T_i+(t+1)\Delta T}{T_i+t\Delta T}}$$ Now I would like to calculate the change in the entropy of the...
38. ### Find the change in entropy for an ideal gas undergoing a reversible process

We know that $$dU=\delta Q + \delta W$$ $$dU = TdS - pdV$$ So from this: $$dS = \frac{1}{T}dU + \frac{1}{T}pdV \ (*)$$ For an ideal gas: $$dU = \frac{3}{2}nkdT$$ Plugging that into (*) and also from ##p=\frac{nRT}{V}## we get: S = \frac{3}{2}nk \int^{T_2}_{T_1} \frac{1}{T}dT +...
39. ### Stability and concavity of the entropy function

I am struggling to understand Callen's explanation for stability, I understand that the concavity of S(U) must be negative because otherwise we can show that this means that the temperature increases as the internal energy decreases (dT/dU<0) but I cannot understand equation (8.1) which...
40. ### I How does the relativity of simultaneity square with thermodynamics?

In special relativity, observers can disagree on the order of events - if Alice thinks events A, B and C are simultaneous, Bob can think A happened before B which happened before C, and Carlos thinks C happened before B which happened before A - provided A, B and C are not causally connected, of...
41. ### I Maxwell's Demon and the Uncertainty Principle

Maxwell's demon measures the position and velocity of the particle. How can it do that when it violates the uncertainty principle? Does that mean uncertainty principle is unavoidable otherwise we will violate II law of thermodynamics as in the case of Maxwell's demon?
42. ### Is randomness real or the inability to perceive hyper complex order?

How did you find PF?: random Brownian motion Is randomness real or is it simply defined as such due to our inability to perceive hyper complex order? Randomness is a troublesome word. I'd feel better if I knew it was an objective phenomenon and not merely a placeholder description of...
43. ### I Explaining atoms and bonding using entropy

I am a biology undergraduate interested in abiogenesis. The entropic explanation for the origin of life is that life is allowed to exist because it increases universal entropy. I am curious about how far we can take this theory down. How can you explain the emergence of atoms and atomic...
44. ### Is Entropy decreased for Free expansion of a Waals gas?

Previous of this problem, there was another problem. that is "What is the change in Temperature of van der Waals gas in free expansion?". I got them. It was C_V dT= -aN^2/V^2 dV Then, I got T=T0-aN^2/2VC_V So i knew that the Temperature is decreased by free expansion in adiabatic process. Then I...
45. ### Von Neumann Entropy time derivative(evolution)

I'm not sure about my proof. So please check my step. I used log as a natural log(ln). Specially, I'm not sure about "d/dt=dρ/dt d/dρ=i/ħ [ρ, H] d/dρ" in the second line. and matrix can differentiate the other matrix? (d/dρ (dρ lnρ))
46. ### Entropy and the Helmholtz Free Energy of a Mass-Piston System

Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...
47. ### I Von Neumann entropy for "similar" pvm observables

The von Neumann entropy for an observable can be written ##s=-\sum\lambda\log\lambda##, where the ##\lambda##'s are its eigenvalues. So suppose you have two different pvm observables, say ##A## and ##B##, that both represent the same resolution of the identity, but simply have different...
48. ### What is the change in entropy for a colloid settling out of solution?

If it occurs spontaneously then it must increase entropy but the possible micro states reduce so what else is occurring to increase entropy
49. ### Meaning of thermodynamic probability

I was studying statistical mechanics when I came to know about the Boltzmann's entropy relation, ##S = k_B\ln Ω##. The book mentions ##Ω## as the 'thermodynamic probability'. But, even after reading, I can't understand what it means. I know that in a set of ##Ω_0## different accessible states...
50. ### Entropy change when melting ice then refreezing the water

##dmL_f= Q \; \; ##,##∆T=\frac{T(v_l-v_s)∆P}{L} \; \;##,##\frac{dmL_f}{T_0}= dS_2 \; \;##,##\frac{dmL_f}{T_1}= dS_1 ##