Thermodynamic and Informational Entropies in Quantum Mechanics

Sebastian Deffner, Steve Campbell

Bryce Weiner

We present a geometric framework that provides a pathway toward resolving quantum measurement through thermodynamic entropy mechanics within causal diamond structures. Entropy mechanics demonstrates that quantum measurement represents the conversion of coherent entropy states (accessible quantum information) into decoherent entropy states (thermodynamically inaccessible information) at precise spacetime boundaries defined by light cone intersections. The universal Quantum-Thermodynamic Entropy Partition (QTEP) ratio Scoh/|Sdecoh| ≈ 2.257 emerges from von Neumann entropy analysis and is characterized by the fundamental information processing rate γ governing all quantum-to-classical transitions without requiring additional empirical input beyond standard quantum mechanics. We add definition to fundamental information units: ebits (entanglement bits) and obits (observational bits), resolving dimensional inconsistencies between thermodynamic entropy and discrete information content. Crucially, causal diamond geometry - the intersection of future and past light cones - provides calculable spacetime boundaries where entropy conversion occurs, with the universal rate γ serving as the fundamental geodesic parameter governing all timelike paths. This architecture features holographic screens of area A(p, q) encoding information and 4-volumes V(p, q) constraining processing capacity. Entropy mechanics offers a substantive refutation of the Many Worlds Interpretation by demonstrating that quantum measurement creates definite outcomes through negentropy generation rather than reality multiplication. The single causal diamond structure provides sufficient geometric and thermodynamic resources for complete energy and information conservation. Gravity emerges as bulk manifestation of information processing optimization on holographic screens, while black holes represent extreme coherent entropy organizations. This framework provides concrete, testable predictions grounded in geometric andthermodynamic principles, with the fundamental insight that quantum measurement dynamics are intrinsically connected to spacetime structure through the universal information processing rate γ governing timelike geodesics.

Austin K. Daniel, Yuri V. Rostovtsev

Gian Paolo Beretta

The nonlinear equation of motion that accomplishes a self-consistent unification of quantum mechanics (QM) and thermodynamics conceptually different from the (von Neumann) foundations of quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but which reduces to the same mathematics for the thermodynamic equilibrium (TE) states, and contains standard QM in that it reduces to the time-dependent Schrodinger equation for zero entropy states is discussed in full mathematical detail. By restricting the discussion to a strictly isolated system (noninteracting, disentangled and uncorrelated), we show how the theory departs from the conventional QSM/QIT rationalization of the second law of thermodynamics, which instead emerges in QT (quantum thermodynamics) as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituent particles. To achieve this, the theory assumes Trρ lnρ B −k for the physical entropy and is designed to implement two fundamental ansatzs: (1) that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated and uncorrelated system admits also states that must be described by non-idempotent density operators (nonzero entropy); (2) that for such additional states the law of causal evolution is determined by the simultaneous action of a Schrodinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituent particles, and in forward time drives the density operator in the 'direction' of steepest entropy ascent (maximal entropy generation). The resulting dynamics is well defined for all non-equilibrium states, no matter how far from TE. Existence and uniqueness of solutions of the Cauchy initial value problem for all density operators implies that the equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also in backward time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates. Zero entropy states as well as a well defined family of non-dissipative states evolve unitarily according to pure Hamiltonian dynamics and can be viewed as unstable limit cycles of the general nonlinear dynamics.

Gian Paolo Beretta

We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy states it reduces to standard unitary QM. The nonlinear dynamical group of QT is construed so that the second law emerges as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituents. It implements two fundamental ansatzs. The first is that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated system admits also states that must be described by non-idempotent density operators (nonzero entropy). The second is that for such additional states the law of causal evolution is determined by the simultaneous action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituents, and (in forward time) drives any density operator, no matter how far from TE, in the 'direction' of steepest entropy ascent (maximal entropy increase). The equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also backwards in time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates.