Assumption of thermal equilibrium for ensembles

Click For Summary
SUMMARY

The discussion centers on the assumption of thermal equilibrium in canonical ensembles, specifically regarding the derivation of distributions and probabilities. It is established that the system must be in thermal equilibrium with the heat bath to utilize these derived distributions effectively. The assumption of constant temperature for the heat bath is acknowledged, but the explicit equality of the system's temperature to that of the heat bath is questioned. Reference is made to H.B. Callen's book on thermodynamics for further insights into the max-entropy principle applied to the combined system of the heat bath and the system.

PREREQUISITES
  • Understanding of canonical ensembles in statistical mechanics
  • Familiarity with the max-entropy principle
  • Knowledge of thermal equilibrium concepts
  • Basic principles of thermodynamics as outlined in H.B. Callen's literature
NEXT STEPS
  • Study the derivation of probabilities in canonical ensembles
  • Explore the max-entropy principle in detail
  • Review H.B. Callen's book on thermodynamics for comprehensive insights
  • Investigate the implications of thermal equilibrium on statistical mechanics
USEFUL FOR

Physicists, students of statistical mechanics, and researchers interested in thermodynamics and the behavior of systems in thermal equilibrium.

Coffee_
Messages
259
Reaction score
2
Take for example a canonical ensemble, to use the derived distributions and probabilities, the considered system has to be in thermal equilibrium with the heat bath.

Where in the derivation of the probabilities and distributions do we usually assume this? There is a point that I can identify assuming a constant temperature for the heat bath yes, but I can't find where we assume that the temperature of the system is equal to the temperature of the heat bath.
 
Physics news on Phys.org
You are deducing the results for a system in thermal interaction with an heat bath by considering the heat bath + the system as an isolated system and using the max-entropy principle for the combined system. See H B Callen's book on thermodynamics.
 

Similar threads

Undergrad Concept of Thermal Equilibrium in the Context of Canonical Ensemble
  • · Replies 5 ·
Replies
5
Views
3K
Thermal Conductivity Problem-- Two Reservoirs
  • · Replies 9 ·
Replies
9
Views
2K
Thermal conductance of an angular section of a disc
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad How Can Internal Energy of the Canonical Ensemble Change (Fluctuate)?
  • · Replies 15 ·
Replies
15
Views
3K
High School Understanding thermodynamic equilibrium
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Connecting the microcanonical with the (grand) canonical ensemble
  • · Replies 37 ·
2
Replies
37
Views
5K
Undergrad Is thermal noise a statistical uncertainty?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Validity of the Boltzmann Distribution
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Paradox: Thermodynamic equilibrium does not exist in gravitational fields
  • · Replies 135 ·
5
Replies
135
Views
8K
Chemistry How to understand the zeroth law through these specific equations?
  • · Replies 3 ·
Replies
3
Views
2K