Undergrad T-symmetry and conservation of energy

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T-symmetry is indeed considered broken due to the violation of CP-symmetry, while CPT-symmetry remains intact. However, this does not imply that energy conservation is affected. T-symmetry's lack of symmetry under time reversal does not negate the conservation of energy, as it is still symmetric under spatial translations. According to Noether's theorem, the conservation of energy is maintained despite the complexities of symmetry violations. Thus, energy conservation holds true even in the context of broken T-symmetry.
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I read that since CPT-symmetry is not broken, and CP-symmetry is, T-symmetry must also be broken, is that correct?

If that is correct, does that mean that energy isn't conserved?
 
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Never mind.
 
T is not symmetric under reversal but still symmetric homogeneous under translations. So by Noether's theorem, energy is conserved.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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