Mixing the two bodies of water has the same effect as the heat transfer of energy from the higher-temperature substance to the lower-temperature substance. The mixing decreases the entropy of the hotter water but increases the entropy of the colder water by a greater amount, producing an overall increase in entropy. For a given substance, the entropy of the liquid state is greater than the entropy of the solid state. Likewise, the entropy of the gas is greater than the entropy of the liquid. Therefore, entropy increases in processes in which solid or liquid reactants form gaseous products.

Mixing is mixing.

By mixing we have a loss of information.

So yes, mixing increases entropy.

Dr Dider Lairez thank you for your contribution to the discussion

The entropy of the liquid phase is higher. The particles are no longer locked in place. Because they are now free to move, they can distribute themselves in more ways. The energy quanta can distribute themselves in a greater variety of ways as well. Changes in phase will lead to changes in entropy. Some phases have larger numbers of microstates and thus higher energy. Solids have the fewest microstates and thus the lowest entropy. Liquids have more microstates and thus have higher entropy. Liquids have more energy and entropy than solids. When there are an increased number of gas molecules, there is also an increase in entropy. When solid is converted liquid, the particles are relatively more free to move and randomness increases. Liquid state has more accessible microstates, so more distribution of energy and hence entropy increases. Mixing the two bodies of water has the same effect as the heat transfer of energy from the higher-temperature substance to the lower-temperature substance. The mixing decreases the entropy of the hotter water but increases the entropy of the colder water by a greater amount, producing an overall increase in entropy. Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder. In another easily imagined example, suppose we mix equal masses of water originally at two different temperatures, say 20.0oC and 40.0oC. The result is water at an intermediate temperature of 30.0Oc. When hot water is mixed with cold water, the mixture attains an intermediate temperature because heat flows from higher temperature to lower temperature. When cold water is poured over hot water, cold water being denser flows to the bottom mixing with the hot water in the process and getting heated up. The entropy increases whenever heat flows from a hot object to a cold object. It increases when ice melts, water is heated, water boils, and water evaporates.

In my opinion, one of the major contribution of information theory to thermodynamics and statistical mechanics is the simplification it allows.

This is the ultimate goal of a theory: allowing an economy of thought.

Dr Didier Lairez thank you for your contribution to the discussion

When hot water is mixed with cold water, the mixture attains an intermediate temperature because heat flows from higher temperature to lower temperature. When cold water is poured over hot water, cold water being denser flows to the bottom mixing with the hot water in the process and getting heated up. When two pure substances mix under normal conditions there is usually an increase in the entropy of the system. This is qualitatively easily visualized in terms of the increased disorder brought about by mixing. Mixing the two bodies of water has the same effect as the heat transfer of energy from the higher-temperature substance to the lower-temperature substance. The mixing decreases the entropy of the hotter water but increases the entropy of the colder water by a greater amount, producing an overall increase in entropy. So generally a mixture will have higher entropy. Before mixing, the solute and solvent are completely separated from each other. After mixing, they are completely interspersed within each other. Thus, the entropy increases. Entropy usually decreases when a gas dissolves in a liquid or solid. Energy from hot water molecules makes solids more soluble. In hot water, molecules are moving around more, so there are more collisions between the water molecules and a solid. Hot and cold water are made of the same type of molecules. Each molecule has one oxygen and two hydrogen atoms. The difference between them is the speed of the molecules jiggling around.