Maximum entropy principle from minimum energy principle

  • #1
Tomas Molina

Homework Statement


Formulate a proof that the energy minimum principle implies the entropy maximum principle. That is, show that if the entropy were not maximum at constant energy then the enrgy could not be minimum at constant entropy. HINT: First show that the permissible increase in entropy in the system can be exploited to extract heat from a reversible heat source (initially at the same temperature as the system) and to deposit it in a reversible work source. The reversible heat source is thereby cooled. Continue the argument.

Reference https://www.physicsforums.com/threa...he-energy-minimum-and-entropy-maximum.915479/

Homework Equations


we wanna prove ds/dx = 0 and d/dx (ds/dx) < 0

The Attempt at a Solution



has something to do with cycles the argument? :c
 

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