Can TdS be computed using an area, time double integral of heat flux density?

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SUMMARY

The discussion centers on the calculation of TdS (temperature times entropy) using a double integral of heat flux density over area and time. Participants explore the implications of this method in the context of a growing black hole, questioning whether the inward flow of heat would result in a negative sign for the integral. The consensus suggests that a dominating black hole could indeed act as a TdS reducer due to the divergence of the field within its surface.

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  • Understanding of thermodynamics and the TdS relation
  • Familiarity with calculus, specifically double integrals
  • Knowledge of black hole thermodynamics
  • Concept of heat flux density in physics
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  • Research the mathematical foundations of double integrals in thermodynamics
  • Study black hole thermodynamics and its implications on entropy
  • Explore the concept of heat flux density and its applications
  • Investigate the relationship between entropy and gravitational fields
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kmarinas86
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Can the TdS by a system be calculated by taking the area, time double integral of the heat flux density?

If so, is it possible that this double-integral would take on an opposite sign if inside there was a dominating, growing black hole, where, I would presume, heat flows inwards, and not outwards? The divergence of the field inside the surface would therefore have an opposite sign, so would a growing blackhole therefore be a TdS reducer?
 
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