Best thermodynamics and statistical mechanics books

Statistical Physics (lecture notes)

It is a precis of tools and effects, instead of a scientific textbook

The concept of probability in statistical physics

Foundational matters in statistical mechanics and the extra basic query of ways chance is to be understood within the context of actual theories are either components which were missed by means of philosophers of physics. This e-book fills a massive hole within the literature by way of offering the main systematic learn thus far of ways to interpret probabilistic assertions within the context of statistical mechanics.

Entropy and Its Physical Interpretation

This article offers a accomplished method of entropy, spotting that it's a suggestion frequently misunderstood. starting with an historic classical point of view, a statistical view then follows to provide a extra actual photograph.

Statistical physics and economics. Concepts, tools and applications

This systematic booklet covers in basic language the actual foundations of evolution equations, stochastic strategies and generalized grasp equations utilized on advanced monetary structures, aiding to appreciate the big variability of monetary markets, buying and selling and communications networks.

Extra info for A treatise on heat: Including kinetic theory of gasses [sic], thermodynamics and recent advances in statistical thermodynamics

Example text

106) −∞ Due to the symmetry property Cαβ (t) = Cβα (−t), the Fourier transforms are ∗ (ω). The Sαβ (ω) are called the spectral functions self-adjoint; Sαβ (ω) = Sβα of the underlying processes. In addition to the classiﬁcation of correlation processes introduced above, the same properties might be investigated in the frequency domain. To this end, we consider again a stationary process in a one-dimensional state space. 105) the important relation τc = S(0). Therefore, we conclude that a convergent behavior of S(ω) in the low-frequency regions indicates a short-range correlation, while any kind of divergence is related to long-range correlations.

This means explicitly Yα (ti+1 ) = Yα (ti ) + aα (Y (ti ))dt + bα,k (Y (ti ))dWk (ti ). 149) k On the other hand, in the Stratonovich interpretation, we take the mean of Y (t) before and after the jump so that Y (τi ) = (Y (ti+1 ) + Y (ti ))/2; namely Yα (ti+1 ) = Yα (ti ) + aα (Y (ti ))dt Y (ti ) + Y (ti+1 ) + bα,k 2 dWk (ti ). 152) are satisﬁed. 139), the coeﬃcients aα (Y ) and bα,k (Y ) can be extended to explicitly time-dependent functions aα (Y, t) and bα,k (Y, t). Such an extension is motivated above all by the fact that possibly a part of the irrelevant variables possesses relatively slow timescales on the order of magnitude of the characteristic time of the relevant quantities.

Therefore, we could possibly use this equation to obtain operator L ˆ Markov . 73) |Y −Z|<ε where we have used the notation ∆Yα = Yα − Zα . 74) for |Y − Z| > ε. We will see later that these quantities were chosen in a very natural way. They can be obtained directly from observations or deﬁned by suitable model assumptions. ˆ Markov by the exclusive use of If we are able to build the Markovian, L these quantities, we have arrived at our goal. Note that possible higher-order coeﬃcients must vanish for ε → 0.