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Also, according to the first law of thermodynamics, work done by external forces will be $dW=-P dV$. … However, energy $U$ must be still a state function, so $dW$ and $dQ$ must compensate somehow to give the first law of thermodynamics: $dU = dQ + dW$ …

After studying statistical mechanics, I understood that thermal fluctuations arise when the system of interest is in contact with a reservoir at some temperature $T$ exchanging energy. Because of this …

What is the physical mechism that disorders magnetic alignment and prevents the material from magnetizing? I believe that thermal fluctuations are responsable but I don't understand what a thermal fl …

I happened to come across the following term while doing an excercise on perturbation theory \begin{equation} H^2=J^2\sum_{<i,j>}\sum_{<k,l>}\sigma_i\ \sigma_j\ \sigma_k\ \sigma_l \end{equation} Whe …

The laws of physics are, at a fundamental level, reversible, so "mapping 2 possible states to 1 firm state" is actually imposible. This is easy to see: if you are in one of the two initial state you c …

Suppose I'm computing the partition function of some system -an Ising Model, for example- \begin{equation} \sum_{x_1,...,\ x_N}e^{-\beta H(x_1,...,\ x_N)} \end{equation} and I want to make a change …

Every answer was really useful so I will try to put it all together in one answer As Abdelmalek Abdesselam said, the partition function can we written as \begin{equation} \tag{1}\label{part} Z=\ …

I'm trying to solve this thermodynamics problem. … Furthermore, there are certain subtleties of thermodynamics that are confusing me. …

Suppose we have a classical Hamiltonian that can be divided into an “easy” part $H_0$ and a “difficult” part $\Delta H$ that depends on a parameter $g$: \begin{equation} H = H_0 + g \Delta H ~. \end{ …

I obtained the Green function at finite temperature for a given system using a simulation. This means I have a list of numbers that represent G(t). Now I would like to use this information to compute …

This is a rather simple question but I haven't found an answer here, I hope it's not a duplicate. Is there a model to explain the formation of a solid? In other words, Is there a way to start a model …

The Ising model has this partition function \begin{equation} Z= \sum_{states}e^{-\beta E}= \sum_{\{\sigma \}}e^{\beta J \sum_{<i,j>}\sigma_i\sigma_j} \end{equation} The internal energy can be calcul …

As you said, in any reversible transformation the system and the reservoir have the same temperature. So, since the definition of entropy needs that you take the system through a reversible path, you …

The answer is that Energy and Mean Correlation are related by the following equation \begin{equation} U= -\frac{q}{2}J N <\sigma_i\sigma_j> \end{equation} where $q$ is the number of neighbours in th …

In thermodynamics, the state of the system can be fully determined by knowing some thermodynamical variables. In most cases, we need three (This depends on how complex the system is). …