What is heat?
Heat is energy delivered by changing the odds over a system's possible arrangements while the energy of each arrangement stays put. Work is the other channel. A piston shifts the energies and leaves the odds alone, while contact with a flame redraws the odds. Sadi Carnot found the ceiling on every engine in 1824 while believing heat was a weightless fluid, caloric, falling from hot to cold like water down a millrace. Caloric does not exist, and every engine since has come in under his ceiling. Both channels come off one rule, the repair step that keeps every settled quantity and redraws the unsettled rest from the settled odds. Shifting energies at fixed odds is work, and redrawing odds at fixed energies is heat. Doing both at once adds a small cross term. Forgotten information leaves a memory as heat.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 23: Why Does Writing Something Down Cost Heat?watch a universe make its own particles