Top 15 Ludwig Boltzmann Quotes

The most ordinary things are to philosophy a source of insoluble puzzles. With infinite ingenuity it constructs a concept of space or time and then finds it absolutely impossible that there be objects in this space or that processes occur during this time.... the source of this kind of logic lies in excessive confidence in the so-called laws of thought.

I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that, when the theory of gases is again revived, not too much will have to be rediscovered.

Bring forward what is true, Write it so that it is clear, Defend it to your last breath!

Which is more remarkable fact about America: that millionaires are idealists or idealists become millionaires.

Available energy is the main object at stake in the struggle for existence and the evolution of the world.

O! immodest mortal! Your destiny is the joy of watching the evershifting battle!

Eleganz sei die Sache der Schuster und Schneider

[W]e will consider the , rather than the velocity of the molecules. Each molecule can have only a finite number of values for its kinetic energy. As a further simplification, we assume that the kinetic energies of each molecule form an ...<math>0,\epsilon,2\epsilon,2\epsilon,...p\epsilon</math>We call <math>P</math> the largest possible value of the kinetic energy, <math>p\epsilon</math>. ...after the collision, each molecule still has one of the above values of kinetic energy.

We assume initially, each molecule is only capable of assuming a finite number of velocities...<math>0, \frac{1}{q},\frac{2}{q},\frac{3}{q},...\frac{p}{q}</math>where <math>p</math> and <math>q</math> are arbitrary finite numbers. ...but after the collision both molecules still have one of the above velocities ...the actual problem to be solved is re-established by letting p and q go to infinity.

We want first to solve the problem... namely to calculate the probability of state distributions from the number of different distributions. We want first to treat as simple a case as possible, namely a gas of rigid absolutely elastic spherical molecules trapped in a container with absolutely elastic walls. Even in this case, the application of is not easy. The number of molecules is not infinite... yet the number of velocities each molecule is capable of is effectively infinite... to facilitate understanding, I will... consider a limiting case.

[I]t is our main purpose not to limit our discussion to thermal equilibrium, but to explore the relationship of this probabilistic formulation to the second theorem of the mechanical theory of heat.

The system of particles always changes from an improbable to a probable state.

According to the second fundamental theorem... change has to take place in such a way that the total entropy of the particles increases. This means according to our present interpretation that nothing changes except that the probability of the overall state for all particles will get larger and larger.

[W]e will be able to identify that quantity which is usually called entropy with the probability of the particular state.

The initial state in most cases is bound to be highly improbable and from it the system will always rapidly approach a more probable state until it finally reaches the most probable state, i.e., that of the heat equilibrium.