Give the mathematical expressions for the thermodynamic and statistical definitions of entropy.

In thermodynamics, entropy (S) is a measure of the disorder or randomness in a system. The thermodynamic definition of entropy is given by:

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dS = _______ ____ _____ _______ ________ ___ ____ _________ ______.
________ _________ ______ __________ ____.
__________ __________ ___ __________ _______ ________ __________ _____ ________.
_________ ______ __________ _____ ______ __________ ___ _____ ____ ______ __________ ______.
________ _____ ___ ___ _________ _______ __________ ______ ______ __________.
___ ___ __________ ______ _________ ______ _________ _________ ____.
____ ____ __________ ____ _____ ________ _________ ___ ____.
__________ _______ ________ _______ _____ ________ ___ ________ ________ ____.
_____ _____ ____ _________ _________.
________ ___ ______ ______ ________ _____ ______ ________ _________ _____ _____ __________.
__________ ___ _____ ______ ________ _______ __________.
_____ ______ ___ _____ ____.
_____ _____ _______ __________ _________ _________.
_______ ________ __________.
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