# Second law of thermodynamics (in terms of entropy)

Is the second law of thermodynamics (in terms of entropy) for closed systems or isolated systems? I thought it must be valid for isolated systems, such as the Universe. But the book Fundamentals of Physics (Halliday, Resnick, Walker) states the law for closed systems. I'm confused.

• I would use these two terms interchangeably. Perhaps you could explain to us what the difference between them is? Apr 25, 2015 at 14:22
• whence did you get the definition for closed? "A closed system in classical mechanics would be considered an isolated system in thermodynamics."en.wikipedia.org/wiki/Closed_system . I think it is unnecessarily confusing to make a distinction . For entropy second law one needs isolation (count microstates) Apr 25, 2015 at 14:56
• Is Wikipedia reliable? Apr 25, 2015 at 15:11
• Why would one use the definition of closed systems in classical mechanics for thermodynamics. That's just silly. Apr 25, 2015 at 17:03
• @Nathaniel That's not only irritating but somehow despite my however many years in physics I've never heard that or figured it out on my own! Sep 6, 2015 at 6:40

In physical science, an isolated system is either of the following:

1) a physical system so far removed from other systems that it does not interact with them.

2) a thermodynamic system enclosed by rigid immovable walls through which neither matter nor energy can pass.

A closed system

In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings. An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter

I am partial to the second law formulated in terms of entropy and of entropy defined with statistical mechanics

The interpretation of entropy in statistical mechanics is the measure of uncertainty, or mixedupness in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the entropy measures the degree to which the probability of the system is spread out over different possible microstates. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and velocity of every molecule. The more such states available to the system with appreciable probability, the greater the entropy. In statistical mechanics, entropy is a measure of the number of ways in which a system may be arranged, often taken to be a measure of "disorder" (the higher the entropy, the higher the disorder). This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system (microstates) which could give rise to the observed macroscopic state (macrostate) of the system. The constant of proportionality is the Boltzmann constant.

where kB is the Boltzmann constant, equal to 1.38065×10^−23 J/K. The summation is over all the possible microstates of the system, and p_i is the probability that the system is in the i-th microstate

As all definitions of entropy are equivalent, this formulation makse clear that the statement of the second law is about isolated systems as defined above.

Following the second law of thermodynamics, entropy of an isolated system always increases. The difference between an isolated system and closed system is that heat may not flow to and from an isolated system, but heat flow to and from a closed system is possible.

When considering microstates heat and energy exchanges are interactions that increase the number of microstates for an isolated systeme, but can leave a closed system.

Thus in contrast to the other answer I conclude that the second law is about isolated systems. It may be that closed is considered a synonym to isolated for the book you are quoting.

2nd law of thermodynamics has many almost equivalent formulations. The traditional ones always assume closed system, isolation is not needed - transfer of energy both via heat and work is allowed.

One formulation:

When thermodynamic system goes from equilibrium state 1 to equilibrium state 2, the entropies of these two states obey the relation

$$S(2) - S(1) \geq \int_1^2 \frac{dQ}{T_r}$$ where on the right-hand side there is an integral over the variable $Q$, the heat transferred. Here $dQ$ signifies energy transferred as heat between the system and the reservoir and $T_r$ is the temperature of the reservoir (the system does not even have to be in a state where it would have a temperature).

The entropy of any equilibrium state $A$ is defined as the integral

$$S(A) = \int_R^A \frac{dU-dW}{T}$$

where $R$ is some appropriate, agreed upon reference state, $U$ is internal energy, $W$ is work done by the system and $T$ is its temperature; the integration is along any path in the thermodynamic state space of the system that connects $A$ with $R$.

2nd law in term of entropy: The second law of thermodynamics can be stated in terms of entropy. If a reversible process occurs,there is no net change in entropy. In an irreversible process, entropy always increases, so the change in entropy is positive. The total entropy of the universe is continually increasing

I have sometimes wondered if the term closed system is occasionally used to mean an isolated system. But if it is the case, this is not universally the case. To return to the Second Law in terms of entropy, the Second Law applies only to an isolated system at equilibrium. For example, if crystallisation occurs in a closed system (such as a metal box) energy transfers to the surroundings and the entropy of the closed system drops. It is only if the box and its surroundings are considered as one (i.e. an isolated system) that the overall entropy is seen to increase.

• This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker. - From Review Aug 19, 2022 at 10:37
• The answer covers whether or not the SL in terms of entropy applies to closed or isolated systems, which was the question asked. As to what my reputation (or yours for that matter) has got to do with anything, I don't know. Aug 20, 2022 at 17:50