I would like to understand how the computation process causes the processor to get hot. I understand that the heat is generated by the transistors.
A transistor (FET, in modern ICs) never switches instantly from full OFF to full ON. There is a period while it's turning on or off where the FET acts like a resistor (even when fully ON it still has a resistance).
As you know, passing a current through a resistor generates heat (\$P=I^2R\$ or \$P=\frac{V^2}{R}\$).
The more the transistors switch the more time they spend in that resistive state, so the more heat they generate. So the amount of heat generated can be directly proportional to the number of transistors - but it is also dependent on which transistors are doing what and when, and that depends on what the chip is being instructed to do.
Yes, manufacturers may position specific blocks of their design (not individual transistors, but blocks that form a complete function) in certain areas depending on the heat that block could generate - either to place it in a location with better heat bonding, or to place it away from another block that may generate heat. They also have to take into account power distribution within the chip, so placing blocks arbitrarily may not always be possible, so they have to come to a compromise.
All current flow in anything that isn't a superconductor generates heat. In chips, it's mostly flowing in aluminium "metal" layers (why not copper? Nasty chemical interaction with other parts of the silicon, it turns out).
What causes current to flow? Every time a transistor changes state, this can be modeled as a capacitor (the FET gate of the driven logic gate plus parasitic wire capacitance) charging/discharging through the wire and output FET of the previous gate. This is "switching" or "dynamic" power. It's proportional to switching speed and the square of the voltage; hence the drive from 5V to 3.3V to 1.8V for better efficiency.
The insulators are not perfect, and in some places are very thin. Transistors may not be fully "off". If a FET has an off resistance of a megaohm, and you put a million of them in parallel, it looks like a 1 ohm resistor. This is "leakage" power. It's proportional to number of transistors.
I spent a decade working at a startup on power optimisation. :) There are a lot of techniques: speed/leakage tradeoffs ("high k metal gate"), turning off parts of the circuit entirely, clock gating, reduction of clock frequency, sizing and placement.
it is simple we know that according to joules law that whenever the electron are flowing through the conductor the heat produced due to the resistance of the material because every conductor have some amount of resistance in it.
If you do the math for a capacitor charging through a resistor, you find the energy lost in the resistor is equal to the energy stored in the capacitor:
$$E = \frac{1}{2} \cdot C \cdot V^2$$
where \$V\$ is the supply voltage of the chip and \$C\$ is the interconnect capacitance plus the total load of the connected MOSFET gate capacitances.
This is true for each node in the CPU circuit. This energy dissipation occurs independent of transistor 'on' resistance provided the FET charges the capacitor nearly fully within the CPU cycle time. It happens for all the MOSFETs switching in the chip. It repeats every time there is a switching event, so it scales with CPU clock speed. So even though the capacitance is tiny, the CPU gets hot, and it gets hot proportionally with the rate of switching events and therefore digital activity. DC current flowing into the FET gates is normally inconsequential.
1) Any time there is current flow, heat is generated by the collisions of the electrons. 2) Yes, generally, the correlation is linear. 3) It is very unlikely that CPU manufactures optimize the position of individual transistors, to minimize the heat generated (they are all inside the same casing).
When a CPU is "idle", although it uses a minimum amount of current, it generates heat. As the processor starts to "process" information, the individual transistors switch states. This switching also generates heat. In addition, the switching frequency affects the heat generation rate, the higher the frequency the higher the heat generation rate. Since the heat dissipation capacity of the chip is fixed, it can overheat if it's operated at a higher frequency than it was designed to operate.
(A & B), this has two inputs and one output. That information that is lost in this process has to go somewhere and becomes entropy (heat)... assuming I understood it enough to describe this. \$\endgroup\$