[AntonioLao]

Originally Posted by GUILLE what are logarithms and logarithmic motion?

Boltzmann used logarithm to describe the motion of entropy in statistical mechanics.
We are now ready to provide a definition of entropy. Let Ω be the number of microstates consistent with the given macrostate. The entropy S is defined as

The quantity k is a physical constant known as Boltzmann's constant, which, like the entropy, has units of heat capacity. The logarithm is dimensionless. This postulate, which is known as Boltzmann's principle, may be regarded as the foundation of statistical mechanics, which describes thermodynamic systems using the statistical behaviour of its constituents.

The logarithm is a way of inverse transformation for finding the exponent when knowing the base and resulting power product. For example, the logarithm of 100 of base 10 is 2. The logarithm of 1 for any base is always zero.

[Guille]

What other things are basic for statistical mechanics?

What is the connection of statistical mechanics to "time"?

[subversion]

if I could go back in time, I would kill the notion of it. Count me in

[Guille]

Originally Posted by subversion if I could go back in time, I would kill the notion of it. Count me in

Great, with you we've achieved the minimum number to make a chat with enough different opinions.

Now, if there is no notion of time there is no notion of motion (it even rimes), but if there is no notion of motion then there is no motion done, for the people don't know there is motion, and, as evolution works, if humans don't move then they will loose the ability to move, and we would now probably be creatures about the size of a cat, but with no extremities (apart form the male sexual one) and around 80% of our body woould be brain. Of course, knwoledge woudl be mnmcuh mor,e but where is everything else? Where are the houses, buildings, cities, sports, arts....? Nowhere.

Kill time, and you will kill existence.

[AntonioLao]

Originally Posted by GUILLE What other things are basic for statistical mechanics? What is the connection of statistical mechanics to "time"?

Some things basic to SM are ensembles, canonical ensembles, grand canonical ensembles, and microcanonical ensembles. The thermodynamic arrow of entropy is associated with the concept of time.

[Guille]

1. What is the relationship between statistical mechanics and thermodinamics, (in particular to entropy)?

2. What are "ensembles" in statistical mechanics?

[AntonioLao]

Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in every day life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum). In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules. In mathematical physics, especially statistical mechanics and thermodynamics as introduced by J. Willard Gibbs in 1878, an ensemble (also statistical ensemble or thermodynamic ensemble) is an idealization consisting of a large number of copies (possibly infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in.

[Guille]

I see, so basically it's "many copies about the movement of energy ofgeneralized large population and their motion. Simple. Complex.

[AntonioLao]

Originally Posted by GUILLE so basically it's "many copies about the movement of energy ofgeneralized large population and their motion. Simple. Complex.

Because of the extremely large populations of elementary particles, both classical and quantum statistical mechanics deal only with averages: average energies, average spin, average mass, average density, average charge, etc. In probability, average is called the expected value of a probability function whether discrete or continuous.

[Guille]

Antonio,

I've just remembered the thread we discussed about "probabilistic mass", so, coudl this avarage masss you talk about have to do with the one we talked about?