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The formula is valid for units of energy

The multiplicity $Ω$ for q units of energy among N equally probable states is given by the expression

This is sometimes called the number of microstates for the system.

Organic life exists because it exchanges energy and diminishes enτροπυ by using the environment it finds itself in. It is only in closed systems that entropy always increases. Crystals appear because the total entropy is conserved or grows, it diminishes in the crystal and increases in the environment.

The error is in the imaginary experiment:

Now we connect the two systems for only an extremely short amount of time, so that they keep their respective volumes and number of particles. Just a long enough timeframe that a small amount of Q can be transferred from the warm system to the cold system.

If they "keep their respective volumes and number of particles" how can a unit of energy be transferred?

The formula is valid for units of energy

The multiplicity $Ω$ for q units of energy among N equally probable states is given by the expression

This is sometimes called the number of microstates for the system.

Organic life exists because it exchanges energy and diminishes entropy by using the environment it finds itself in. It is only in closed systems that entropy always increases. Crystals appear because the total entropy is conserved or grows, it diminishes in the crystal and increases in the environment.

The error is in the imaginary experiment:

Now we connect the two systems for only an extremely short amount of time, so that they keep their respective volumes and number of particles. Just a long enough timeframe that a small amount of Q can be transferred from the warm system to the cold system.

If they "keep their respective volumes and number of particles" how can a unit of energy be transferred?

The formula is valid for units of energy

The multiplicity $Ω$ for q units of energy among N equally probable states is given by the expression

Organic life exists because it exchanges energy and diminishes enτροπυ by using the environment it finds itself in. It is only in closed systems that entropy always increases. Crystals appear because the total entropy is conserved or grows, it diminishes in the crystal and increases in the environment.

The error is in the imaginary experiment:

Now we connect the two systems for only an extremely short amount of time, so that they keep their respective volumes and number of particles. Just a long enough timeframe that a small amount of Q can be transferred from the warm system to the cold system.

If they "keep their respective volumes and number of particles" how can a unit of energy be transferred?

The formula is valid for units of energy

The multiplicity $Ω$ for q units of energy among N equally probable states is given by the expression

This is sometimes called the number of microstates for the system.

Organic life exists because it exchanges energy and diminishes enτροπυ by using the environment it finds itself in. It is only in closed systems that entropy always increases. Crystals appear because the total entropy is conserved or grows, it diminishes in the crystal and increases in the environment.

The error is in the imaginary experiment:

Now we connect the two systems for only an extremely short amount of time, so that they keep their respective volumes and number of particles. Just a long enough timeframe that a small amount of Q can be transferred from the warm system to the cold system.

If they "keep their respective volumes and number of particles" how can a unit of energy be transferred?

The formula is valid for units of energy

The multiplicity W for q units of energy among N equally probable states is given by the expression

Organic life exists because it exchanges energy and diminishes energy by using the environment it finds itself in. Crystals appear because the total entropy is conserved, it diminishes in the crystal and increases in the environment.

The error is in the imaginary experiment:

Now we connect the two systems for only an extremely short amount of time, so that they keep their respective volumes and number of particles. Just a long enough timeframe that a small amount of Q can be transferred from the warm system to the cold system.

If they "keep their respective volumes and number of particles" how can a unit of energy be transferred?

The formula is valid for units of energy

The multiplicity $Ω$ for q units of energy among N equally probable states is given by the expression

Organic life exists because it exchanges energy and diminishes enτροπυ by using the environment it finds itself in. It is only in closed systems that entropy always increases. Crystals appear because the total entropy is conserved or grows, it diminishes in the crystal and increases in the environment.

The error is in the imaginary experiment:

Now we connect the two systems for only an extremely short amount of time, so that they keep their respective volumes and number of particles. Just a long enough timeframe that a small amount of Q can be transferred from the warm system to the cold system.

If they "keep their respective volumes and number of particles" how can a unit of energy be transferred?