Decoding information causes the entropy production of the system to be negative, therefore as we have shown above this causes the system to perform more work and, in turn, this leads to having an efficiency greater than that of Carnot. Del Rio et. al31 have shown that erasing a system, which is coupled strongly with another system (a quantum memory), may cause the conditional entropy of the system to be negative and this negative entropy will lead to extracting work from the system,
https://www.nature.com/articles/s41598-021-81737-z
the internal energy is decoded to be used by the system to perform more work than what is expected and this additional work leads to having quantum engines with efficiencies greater than that of Carnot.
a quantum thermodynamic force is responsible for encoding and decoding information even when a feedback controller outside the system is involved in the process.
https://spp.fas.org/eprint/quantum.pdf
https://personal.lse.ac.uk/robert49/PPB/pdf/Penrose1979a.pdf
https://arxiv.org/pdf/2102.12214.pdf
https://royalsocietypublishing.org/doi/10.1098/rspa.2015.0670
an interference function that takes account of the non-commutativity
These remarkable results manifest a fundamental difference between quantum states in time and space.
just as matter can be represented as existing only in a finite region of space, it can also be represented as existing only for a finite interval of time. Clearly, the price we pay for this symmetry is absence of the conservation of mass. However, with the violation of T symmetry, dramatic differences between the representation of quantum states in space and time arise through the quantum interference between different paths. The state (and the matter it describes) is found to persist over an unbounded range of time values. This result gives a new appreciation of conservation laws: while they may be due to deep principles, they are not manifested unless the state persists over a sufficient period of time. The Schrödinger equation of conventional quantum mechanics, where time is reduced to a classical parameter, also emerges as a result of coarse graining over time. As such, T violation is seen in the new formalism as being responsible for fundamental differences between space and time in conventional quantum mechanics.
It appears, therefore, that T violation is also responsible giving time a direction (in the sense of orientating time away from the occurrence of |ϕ〉).
In conclusion, the importance of Feynman's sums over paths for describing quantum phenomena is well beyond doubt [43]. A distinctive feature of the quantum virtual paths in the new formalism is that they explicitly take into account the violation of T symmetry. The new formalism has the advantage of giving time and space an equal footing at a fundamental level while allowing familiar differences, such as matter being localized in space but undergoing unbounded evolution in time, to arise phenomenologically due to the fact that T violation is a property of translations in time and not space. As such, the violation of the discrete symmetries is seen to play a defining role in the quantum nature of time and space.
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