Loosely expressed, the basic premiss of the classical western science goes as follows:

“…..Science is a set of laws which tells you how your system will evolve, given the present conditions..”

One of the most important laws modern physics is the “conservation of energy”. This law tells us that all physical systems are associated with a quantity, called “the energy of the system”, which is always conserved no matter how the system evolves. A system may have many different types of energies (mechanical, heat, electrical, chemical..) and these may convert into each other during system’s evolution.. But, they are all measured in joules, and their sum always remains constant..

To be crystal clear, let us imagine some scenarios:

FIRST SCENARIO

Assume we have thrown a ball straight into air with speed $v_0$. As the ball leaves our hand, it has a kinetic energy of $\frac{1}{2}mv^2$. Then, as is rises, its kinetic energy converts into potential energy. The highest point $h_0$ that the ball reaches can be calculated as

\begin{eqnarray}

\frac{1}{2}mv_0^2 = \frac{1}{2}mv^2 + mgh = mgh_0

\end{eqnarray}

In this example, the energy remains mechanical. What about a system in which both mechanical and heat energy exists together?

SECOND SCENARIO

Consider a ship moving on the sea with velocity $v_0$. Let the engines of the ship are shut down. What happens? When the engines are shut down, the ship has kinetic energy $\frac{1}{2}mv_0^2$. Slowly, ship comes to a stop via friction. What happens to its kinetic energy? The kinetic energy is converted into heat, which results in a tiny increase of the oceans temperature, $\Delta T$.

\begin{eqnarray}

\frac{1}{2}mv_0^2 = Mc \Delta T

\end{eqnarray}

Here $M$ is the mass of the ocean, $c$ is the specific heat of seawater. As $M$ is huge, $\Delta T$ is very small.

THIRD SCENARIO

Can we think the second thought experiment experiment in reverse? Consider a ship standing in the middle of the ocean whose engines are not working. Some of the heat energy in the ocean flows into the ship, and there it is converted into the mechanical energy, and moves the ship with the speed $v_0$?. As this happens, the oceans must cool a tiny temperature $\Delta T$ as heat is extracted from it and transferred tothe ship to move it. Energy balance equation is

\begin{eqnarray}

\frac{1}{2}mv_0^2 = Mc \Delta T

\end{eqnarray}

which is the same with the second thought experiment. But this time energy is transferred from the ocean to the ship.

FOURTH SCENARIO

We put a warm bucket of water in our garden. The bucket slowly cools, and in time comes to the same temperature with the environment. Extra heat energy stored in the water leaks into the air and warms it a little bit.

FIFTH SCENARIO

We put a bucket of water who has the same temperature with the envirpnment. Then the heat energy flows from the environment to the bucket and bucket’s temperature increases while the environment cools a bit.

Energy is conserved in all these scenarios. But we know from our life’s experience that 1st, 2nd and 4th scenarios are our daily experience, while events similar to 3rd and 5th scenarios are never encountered in real life.

Moving objects, when left to their own, come to a rest and warmer objects cool to environment’s temperature. Resting objects never start to move or get warmer/cooler on their own. Note that energy is conserved in all these cases. Therefore the law of conservation of energy is insufficient to describe nature. There must be something more in nature which weed out these. This “something” is called Entropy.

In addition to energy, we need to assign a second quantity to physical systems: Entropy. Entropy is a strange beast. While the total energy of a system never changes and always conserved, entropy of a system must either remain constant or increase. Hence it is more akin to an industrial engineering quantity than a physics quantitiy. As we will see shortly that

- In the first scenario, the energy and entropy remains constant. Hence the events described therein is possible.
- In the second scenario, the energy is conserved and entropy of the system is increased. Hence the events described therein is possible.
- In the scenario, energy is conserved and entropy of the system is decreased. Hence the events described therein is impossible.