# Understanding chemical potential in AdS/CFT

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I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice references or briefly discuss about it intuitively. Actually I came across it again in the context of AdS/CFT. It will be really helpful if it is discussed in holographic context.

This post imported from StackExchange Physics at 2015-08-25 07:26 (UTC), posted by SE-user pinu

edited Aug 25, 2015

In this case isn't chemical potential simply the energy required to increase the number of particles or qubits? If you like intuitive analogies, John Baez has compiled a good description including chemical potential: https://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/

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$\mu =\frac{\partial G}{\partial N}$ i.e. it is free energy per particle in an ensemble, or energy needed for a particle to add it to the system so that the system will stay in equilibrium. (Some call it the Gibbs free energy/enthalpy. Free energy is usually the name for the Helmholtz free energy). Formal definition -

$$G(T,P,N)=E(T,P,N)+P\cdot V(T,P,N)-T\cdot S(T,P,N)$$ so the equilibrium state is given for minimal value of $G$. If you put in contact 2 closed systems with $G_1(T_1,P_1,N_1)$ and $G_2(T_2,P_2,N_2)$ , the combined system system will seek a new equlibrium with maximal entropy and minimal $G$ - $$G^*(T^*,P^*,N^*)=G_1^*(T^*,P^*,N_1^*)+G_2^*(T^*,P^*,N_2^*)$$

Because of the maximal entropy principle - one of the ways the system tries to minimize $G$ /maximize entropy is by flow of particles from one system to another. The particles will flow from system with high value of $\mu$ to the system with low value - that according to the principle of minimizing free energy in the system.

This post imported from StackExchange Physics at 2015-08-25 07:26 (UTC), posted by SE-user Alexander

answered Jun 5, 2015 by (20 points)
Thanks for the answer. Actually I was looking for a more intuitive way of understanding chemical potential and specially in the context of AdS/CFT.

This post imported from StackExchange Physics at 2015-08-25 07:26 (UTC), posted by SE-user pinu

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