Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 3 research declarations. Search 10,000 more complete Mathlib declarations.

1 topic

3 results

Clear filters
Project-declaredLean 4.32.0

Entropy A eq entropy Z

MicroHamiltonian.entropy_A_eq_entropy_Z

Plain-language statement

The two definitions of entropy, in terms of T or β = 1 / T, are equivalent.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.28.0

Entropy A eq entropy Z

MicroHamiltonian.entropy_A_eq_entropy_Z

Plain-language statement

The two definitions of entropy, in terms of T or β, are equivalent.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Β eq deriv S U

MicroHamiltonian.β_eq_deriv_S_U

Plain-language statement

The "definition of temperature from entropy": 1/T = (∂S/∂U), when the derivative is at constant extrinsic d (typically N/V). Here we use β instead of 1/T on the left, and express the right actually as (∂S/∂β)/(∂U/∂β), as all our things are ultimately parameterized by β. This identity requires the denominator ∂U/∂β to be nonzero.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record