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Is the thermal equilibrium state the state of maximum entropy? Is it a consequence of the second law of thermodynamics?

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Is the thermal equilibrium state the state of maximum entropy?

Entropy can always be made higher, just by adding some heat with no work or performing work irreversibly on the system with no heat transfer.

What is meant by the principle of maximum entropy is that given some constraints like total volume, energy and number of particles of single species, the other thermodynamic variables in equilibrium are such that any change of their value (while the constraints are fixed) leads to decrease of entropy.

Is it a consequence of the second law of thermodynamics?

State of equilibrium is a basic idea thermodynamics is built upon, usually introduced before 2nd law.

The thermodynamic principle of maximum entropy is surely connected to 2nd law of thermodynamics, but I think it is possible one has to make other assumptions besides 2nd law to arrive at this principle there.

In statistical physics, maximum entropy principle is a different thing (about different concept of entropy in different context) and can be argued to stand on its own. A special version of second law of thermodynamics can then be derived from this principle (Edwin Jaynes explained how) if some other assumptions are made (one that comes to mind is that system has to obey the Liouville theorem).

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