# How does entropy increase over time?

According to 2nd law of thermodynamics,

In an isolated system entropy increases over time. In an open system entropy might seems decreases but combined result of all related events results in overall entropy increase.

Now lets say, a shuffled deck of playing cards. If I sort the cards it seems entropy will decrease. So, what are then the related events which increase the overall entropy?

• Can you explain why you think the card deck is a closed system? – BioPhysicist Apr 28 at 1:44
• I assume the incident happened within a closed room in between me and the cards so thats in the closed system. Anything wrong in my thoughts? @Stevens – Sazzad Hissain Khan Apr 28 at 2:03

To organize the cards you have to give up energy by moving the cards around (your arms moving for instance). You will also generate heat $$\delta Q$$, and your internal entropy will increase, $$$$dS_{\text{you}} > {\delta Q \over T}.$$$$ Second law of thermodynamics is precisely the statement that the total entropy will increase, $$$$dS_{\text{you}} + dS_{\text{cards}} > 0.$$$$ So you can only reduce the entropy of the cards by increasing your own or your surroundings by a greater amount.

Your cells have a bunch of energy in well organized structures called sugars. By the time you finish shuffling, you have turned them into more disorganized CO2 and H2O. The amount of entropy reduced in the card deck is less than the amount of entropy increased in these molecules.

• To put numbers on it, a card deck has $52!$ possible arrangements. The entropy that must be decreased is on the order of $\lg 52! \approx 225$ bits. The entropy that is generated by dissipation of, say, one joule of energy at human body temp (310 K) is on the order of $\frac{1\ \mathrm{J}}{k_B \cdot (310\ \mathrm{K}) \cdot \ln 2} \approx 3.4 \times 10^{20}$ bits. Clearly one number is vastly larger than the other. – The_Sympathizer Apr 28 at 3:21
• Yes, hypothetically your numbers work as an example. But we cant say it costs one joule for sure. – Sazzad Hissain Khan Apr 29 at 15:03

The system is an open system. You are inputting energy. It increases the overall entropy or "disorder" of the universe because now the energy that was used to shuffle the cards was converted into heat and light energy which is a disordered form of energy.

Those "related events" take place within the "machine" which causes the entropy decrease.

That "machine" is the human body.

The body is constantly consuming nutrition, fats, protein etc. - breaking down systematic low-entropy entities and released bound energy, causing an increase in entropy - in order to perform entropy-decreasing actions such as sorting mixed playing cards.

Any mechanical engine does the same thing, by burning fuel, breaking down the molecules and releasing volatile gasses and bound energy.

The 2nd law of thermodynamics states that the entropy increase due to these events-within-the-body is larger than the entropy decrease they cause.