Hot answers tagged

13

I personally find the terms consistent. Think of the entropy as Boltzman proposes: $S=k \, \ln W$ Meaning high entropy states can be realized via many different configurations. Truly ordered state (assume you arrange a sculpture from atoms) can be realized via much smaller number of microscopic states. So again, equilibrium is not order - it is a mess.


8

What you are missing is the microscopic definition of entropy, once you know that, you will understand why people say that entropy is disorder. Equilibrium as order First, let's address your valid intuition that equilibrium as a form of order. Indeed, if everything is in thermal equilibrium, you just need to measure the temperature somewhere, and then you ...


6

First of all as stated by Madan Ivan: equilibrium is not order. But you can get certain systems that are in a meta-stable "local" equilibrium (here meaning that you need some energy to move it from there), for example a crystal. These can be highly ordered. Intuitively: if you smack the crystal with a hammer it breaks to pieces. This brings your closer to ...


5

For any function of multiple variables, say, $f(x, y, z, \ldots)$ you can always write the following: $df = \big( \frac{\partial f}{\partial x} \big)_{y, z, \ldots} dx + \big( \frac{\partial f}{\partial y} \big)_{x, z, \ldots} dy + \big( \frac{\partial f}{\partial z} \big)_{x, y, \ldots} dz + \ldots$ In fact, the constancy of the other variables is ...


4

Please note that the second law of thermodynamics applies to isolated systems. Life, the simplest cell, is an engine for reducing entropy in its volume and increasing entropy in its surroundings, so life is not limited by entropy because it develops within a larger medium, which can be considered as isolated. Crystals also do the same, when something ...


3

Entropy is not disorder; it is a lack of information. Consider the entropy formula $S = k_b \log \Omega$. Here, $\Omega$ is the number of microstates (sets of particle positions/momenta) corresponding to an observed macrostate (something macroscopic we can observe, like 'the gas has volume $V$ and pressure $P$). What this formula means is that the entropy ...


3

This is a question that cannot be answered without understanding what time is. And I think the best we can say is that time is a quantity we use to compare events. But the compared feature is the ordering. Bearing that in mind, we cannot say much about its reality, even less about its direction. In other words, despite the fact that you can order events, ...


3

Your question is how the differential quotient $\frac {dU}{dS}$ can mean anything in equilibrium when the quantities $U$ and $S$ are supposed to be constant, it is equilibrium after all... Indeed, $dU$ or $dS$ do not mean changes over time in a physical sense, ie., over time during some process, Instead they mean the differentials of the respective ...


2

The 2nd Law of Thermodynamics is based on an overwhelmingly extensive body of empirical evidence on how thermodynamic systems behave. There are many different statements of the 2nd Law, and all of them are equivalent to one another. Once one of these has been specified, all the other follow. One such statement says that heat cannot flow spontaneously from ...


2

Let us start with an example, called Langevin paramagnetism, where the magnetic moment is described classically, as a vector in three dimensions. Calling $\vec\mu$ this moment, $\vec B$ the magnetic induction and $\theta$ the angle between $\vec\mu$ and $\vec B$. The probability density of the angle $\theta$ is $\rho(\theta)=\frac{1}{\mathcal Z}\exp(\beta\mu ...


2

While a funny-looking coincidence, this is not a valid alternative expression for entropy in general, since the entropy of a probability distribution (which are what rigorously hides behind the strange word "macrostate") is more generally given by $$ S = - k_B \sum_i p_i\ln(p_i) \tag{1}$$ and becomes only $$S = k_B \ln(\Omega) \tag{2}$$ in the case of a ...


2

The equilibrium thermodynamic state of a single phase substance of constant composition is determined by specifying two intensive properties. Note that, from the equation of state, V and T uniquely determine P (where V is the specific volume).


2

As mentioned in a comment, entropy cannot decrease in a closed system. When you are considered life on Earth, it is not a closed system. Energy comes into the earth from the sun and radiates away from the earth as heat. In thermodynamics, we normally consider mostly engines because they are really simple in comparison to other systems. If we ignore the ...


1

The second law of thermodynamics says that order always decreases in a system. This is incorrect. My air conditioner alone proves that this statement of the second law of thermodynamics is incorrect. I live in Houston, TX; I rely on my air conditioner for about six months of the year. My air conditioner does not violate the second law of thermodynamics. ...


1

A macrostate is a set of microstates. Some microstates are thermal, others are not. Without the assumption of being in thermal equilibrium you can't assume anything since any possible microstate is possible. And lots of possibilities macrostates could be picked. Usually you want to group your macrostates according to a state variables such as pressure, ...


1

You say: We shouldn't care about how we reached that equilibrium In fact the entire point of the example is that we do. I shall try to explain why. Jaynes and Gull both work in the framework of Bayesian inference (I can recommend the introductory text: http://www.amazon.co.uk/Data-Analysis-A-Bayesian-Tutorial/dp/0198568320. The title may seem ...


1

It depends what you mean by immortal: If it means to transcend time, can anything wholly mortal or finite transcend time? Even in religous philosophies already some divine element, spark or breath ie something transcendent or immortal in this sense is mixed in with the human clay ie mortal or finite. If it means to to last as long as time lasts - at least ...


1

From a mathematical perspective this means that it is not differentiable. The problem is that you need the discreteness to be able to count states. If you replace the discreteness by something smooth you get something differentiable, but your definition of entropy no longer makes sense. This is just one of the points where mathematicians cringe, but it works ...


1

The reason why heat cannot flow from cold to warm is that the change in entropy will become negative, and that doesn't happen in a closed system. Negative entropy is by definition not possible. Here's why: Alternative example: gas in a box I think entropy gets a little more intuitive if we think of it in terms of statistical mechanics. If we imagine a box ...


1

Time is just a scale we use to measure the rate of processes or to measure the interval between 2 events. Time is not a stand-alone entity and it does not exist alone independently. All the means (like clocks) we employ to measure Time use some standard physical changes as their fundamental measuring units of Time. So Time has no direction of its own, ...


1

The entropy law can be (comically) reinterpreted like "equilibrium is a state of maximum possible disorder under given physical constraints". So... things keep getting worse until it's as bad as it can get. Intuitively, large entropy means that things look more or less the same (macroscopically) for many different microscopic realizations. When the system ...



Only top voted, non community-wiki answers of a minimum length are eligible