Would someone explain entropy in simple terms please. Thanks.

Suppose that you want to use the laws of physics to explain the properties of macroscopic objects, like cars, buildings, airplanes, etc.

Then the problem you face is that the laws of physics tell you about how the fundamental particles interact with each other, while you are only interested in macroscopic properties of a system.

Then, if it were possible to rewrite the laws of physics in terms of only the macroscopic variables (like the center of mass of cars etc.) then the fact that everything consists of elementary particles would not matter.

But it turns out that this is not possible. To see this, consider the kinetic energy of a system of particles. The kinetic energy of the center of mass is not the sum of the kinetic energy of all the individual particles. This then means that energy in the center of mass motion can be "lost" as "internal energy".

This means that one cannot describe macroscopic system in terms of only the center of mass motion of objects. The microscopic details of the system are relevant to some extent.

Then, short of describing a system in terms of all the particles it consists of, we can describe the miscoscopic degrees of freedom statistically.

Now, unless you know the probabilities, you cannot make statistical predictions. It turns out that all possible states an isolated system can be in are equally likely.

Then one defines the entropy as:

S = k Log[Omega(E)]

where Omega(E) is the number of states the system can be in given that its internal energy is E and k is Boltzmann's constant.

To see what use this is consider two systems one with internal energy E1 and the other with internal energy E2. System 1 can be in Omega1(E1) number of states, system 2 can be in Omega2(E2) number of states. This then means that the number of states the combined system can be in is given as:

Omega1(E1)*Omega2(E2)

Suppose we bring the two systems in contact. Then, you know that heat can flow between the two systems. But this process can now be explained as follows. All the states of the combined system are equally likely, but they only become accessible if we allow energy to be exchanged from bith system (i.e. we allow heat to flow from one to the other system).

Then the fact that all states are equally likely means that that particular energy distribution that can be realized in the most way is the most likely situation for the combined system. This then means that when the two systems are combined, heat will flow until

Omega1(E1)*Omega2(E2)

becomes as large as possible.

The total energy E = E1 + E2 will remain constant. So, we can find the maximum by putting E2 = E - E1 and differentiatin g w.r.t. E1. It is convenient to take the logarithm. You fund that:

d Log[Omega1(E1)]/dE1 =

d Log[Omega(E2)]/dE2

Or, in terms of entropy:

dS1/dE1 = dS2/dE2

One now defines the temperature T of a system as:

1/T = dS/dE

So, the above equation says that in thermal equilibrium, temperatures become the same. And the definition of temperature implies that:

dS = dQ/T

where Q is energy that is supplied to a system in the form of heat.

Thank you for giving such a detailed answer.

Of course! I'd be happy to explain entropy in simple terms.

Entropy is a concept that comes from thermodynamics, but it can also be applied to other fields like information theory. In thermodynamics, entropy is a measure of the disorder or randomness in a system. The higher the entropy, the more disordered and random the system is.

Think of a messy room compared to a clean and organized room. The messy room has higher entropy because things are scattered randomly and there is no specific order. On the other hand, the clean room has lower entropy because everything is in its proper place and there is order.

In a thermodynamic system, entropy increases as energy disperses or spreads out. For example, if you have a hot object in contact with a cold object, heat energy will flow from the hot object to the cold object until both objects reach the same temperature. This energy transfer increases the entropy of the system because the energy becomes more evenly distributed.

Now, here's how you can calculate entropy in a simple way: In some cases, you can calculate the entropy of a system by dividing the heat transfer (Q) by the temperature (T). So the equation for entropy change (ΔS) can be expressed as ΔS = Q/T.

This equation helps quantify the change in entropy of a system due to heat transfer. The larger the heat transfer or the smaller the temperature, the greater the change in entropy.

So, in layman's terms, entropy can be understood as a measure of randomness, disorder, or energy distribution within a system.